Higgs Field

 When you step on a scale and look down at the number that shows up, what that number is telling you is how much force the mass of your body exerts on the ground. It's simple Newtonian mechanics. Force equals mass times acceleration. Gravity exerts the acceleration on the mass of your body, which creates a force. That's your weight. So weight is probably easy enough to understand, but mass is a little more nebulous. If you were floating in space, far away from Earth, you would essentially have no weight. But you would still have the same mass as you did standing on that scale. Where does the mass of your body come from? Well, the mass comes from all the atoms in your body that individually have a mass. Where does an atom's mass come from? Well, this is interesting because the mass of atoms at its core is really energy. In fact, all mass is energy. This is exemplified in Einstein's famous mass energy equivalence equation E equals mc squared.

 Massis interchangeable with energy, andthe constant c squared, or speed of light squared, is the conversion factor. So where is the energy of the atom coming from? Well, 99 % of the mass of an atom is contained in the binding energy within the nucleus. This energy is a result of one of the four fundamental forces of nature, called the strong force, which keeps the protons and neutrons glued together in the nucleus of atoms. That's where most of your body's so -called mass resides.

But it turns out that some of your mass, about 1%, is contained in the mass of the subatomic particles that make up the atoms. These are the electrons that form a cloud around the nucleus, as well as the quarks that make up the protons and neutrons. So now the question is, how did these subatomic particles have an intrinsic mass? If mass is energy, then what is the mechanism that confers this energy to these fundamental particles? This is where the Higgs field comes into the picture.

 This field is everywhere in space -time, but most explanations of how this field confers mass can't avoid getting highly technical, talking about symmetry breaking and other advanced mathematical concepts. In this video, I'm going to attempt to explain how the Higgs field confers mass in an intuitive way. So whether you're a math geek or not, you will hopefully get a very good intuitive understanding of what's really going on. That's coming up, right now. I've been wanting to make this video for a while, and I think you're going to find it really interesting. Before we get into it though, I want to thank our sponsor Blinkist that helped make this video possible. This is the one app that saves me more time than any other. Now, as you might suspect, I'm a voracious reader. Blinkist gives me access to over 5 ,500 non -fiction books and podcasts that I can read or listen to in only about 15 minutes. Now, it's not a replacement for reading the whole book, but it allows me to understand the most important things from them.

For example, I just finished listening to a book called The Latte Factor. It's about how making small changes in your life can result in huge outcomes over time, like drinking less latte. What I learned is how life is really a series of baby steps that may not have an immediate payoff, but over time can help you achieve big goals. And my goal this year is to improve my mental and physical health. Blinkist will help me reach that goal, and it can do the same for you. Whatever you want to achieve for yourself is available to you at Blinkist. Right now, Arvin Ash viewers get a whopping 30 % off your subscription, and you can enjoy two memberships for the price of one in a new feature called Blinkist Connect. This allows you to recommend and share your favorite titles with a friend or loved one. Your first 7 days is absolutely free. When you sign up, I highly recommend you click the link in the description. I think you'll be very impressed. Now, where were we? To understand how the Higgs field works, we have to first understand what our best theory describing all the matter in the universe, the standard model of particle physics, is trying to tell us.

 This theory describes all fundamental particles in the universe as excitations in quantum fields. So for example, an excitation of the electromagnetic field would be a photon. An excitation of the electron field is an electron. And an excitation of the quark field would be a quark, etc. These are waves, but when they are well localized as in a measurement, they appear to us as particles. These fields span all of space -time in all directions. The animation you're seeing here is a 2D representation for visualization, but the fields would be in three dimensions. Every type of matter and force particle has its own field. So all the fundamental particles of the standard model would be represented by different fields. All these fields, when they are in their ground state, that is their lowest energy state, even when no excitations or particles are present, always have some vibration. Due to the Heisenberg uncertainty principle, particles are constantly being created and annihilated.

These are virtual particles that exist for such short periods of time that they cannot be measured. They borrow energy from the vacuum when they are created and give it right back very quickly when they are annihilated. But this flurry of energetic activity for each field collectively adds up to zero net real particles. Real particles are created only when enough energy is transferred to these fields from some other field to cause an excitation.

 These excitations are the real particles. And since these are quantized fields, any excitation occurs only in set quantities. So for example, an excitation of the electron field would have to occur in integer multiples of 0 .511 MeV, which is the mass of one electron. So the field can have energy of 1 .022 MeV, which would be the energy of two electrons, or any other multiple of 0 .511, but not for example 0 .7 MeV, which would not be an integer multiple of 0 .511. But the electron only has this intrinsic mass of 0 .511 MeV because of its interaction with the Higgs field. Without this interaction, an electron would be massless. It would have energy, but only in the form of momentum, just like photons. This massless electron would be like a charged photon and move at the speed of light.

 In fact, without the Higgs field, all the other fundamental particles of the standard model would also be massless, with the possible exception of neutrinos. So the question is, how does this mass come about? To answer this, we have to understand the concept of vacuum expectation value of the various fields. What does this mean? Let's imagine for a minute, as if there were no Higgs field. If we then took any of the fields and put them inside an empty box, like the electron field, and if we then weighed that box, we would find that box would have no weight. In other words, the field would have no mass, even though the virtual electrons would be present throughout it. Similarly, all the other fields of the standard model would also have no mass inside the empty box, just quantum fluctuations. But here's the big kicker. There's an exception to this rule. The Higgs field. It's unique because the Higgs field in empty space, unlike every other field, has a net positive mass. Its mass is not zero in empty space. If we were to weigh the box with the Higgs field inside, it would have a weight. The Higgs field in empty space has a mass. This is called the vacuum energy. A more technical term for this is the vacuum expectation value, VEV, of the Higgs field. It is non -zero. It is in fact 246 Giga electron volts, or GeV. This is just the value that we would expect the Higgs field to have when it is in its vacuum state, or in its lowest energy state. Now, as I stated earlier, quantum fields can interact with each other. What this basically means is that anything that interacts with the Higgs field now effectively interacts with this new vacuum expectation value. And that interaction means energy.

And since energy and mass are equivalent, the form this interaction energy takes is indistinguishable from the form of energy associated with a rest mass. So when a fundamental particle interacts with the Higgs field, it gains an energy, or intrinsic mass. Without the Higgs field, forexample, the electron would be massless, like photons, and travel at the speed of light. However, since the electron is coupled to a field with positive value everywhere in the universe, individual electrons are constantly interacting with this Higgs field. This constant interaction effectively slows the electron down. So if you apply a force to an electron, youcan imagine a sort of pushback from the Higgs field that causes the electron to resist acceleration. This property is what we call inertial mass. The electron's behavior in the vacuum is that of a particle with a well -defined rest mass of 0 .511 MeV.

 This rest mass is determined by the strength of the coupling, or interaction, between the electron and the Higgs vacuum expectation value. It's like the mass of the Higgs field is shared with any other field that interacts with it. How much mass an excitation or particle in any given field has depends on its coupling constant. The fields of all massive particles are coupled to the Higgs to some degree.

 The larger this coupling is, the more mass its particles will have. Without the Higgs field, none of the other particles would have an intrinsic mass. The Higgs field is like a thick gravy, and if you try to run a spoon through it, it feels heavy, compared to moving the spoon through the air. So every elementary particle with mass interacts with this gravy in some way. The particles of the Standard Model that have mass such as electrons, quarks, and W and Z bosons are coupled to the Higgs field. While the fields of massless particles, like photons and gluons, are not. So why are some particles coupled, meaning why do some particles interact with the Higgs field, while others do not? We're not sure. This just appears to be the way the universe works. The photon happens to be one of the particles that does not interact with the Higgs field, and so it remains massless and moves at the speed of light.

 The mechanism of the Higgs field giving out mass to other particles is called symmetry breaking. This is a complex subject, but if you want to know more about symmetry breaking, I made a video about it right up here. Now I should add a note about neutrinos. The Standard Model predicts that they should be massless, but measurements seem to indicate that they do have a very tiny mass. We don't know the origin of this mass. It could be that they also interact with the Higgs, but no one really knows for sure.

 Now I want to reiterate what I said at the beginning. The Higgs field is only responsible for about 1 % of the mass of all the matter in the universe that we can see. The vast majority of this mass is due to the energy of the strong force, which keeps the nuclei of atoms tightly glued together. Yet, this 1 % is essential to have the kind of universe we have. In a simple hydrogen atom, for example, the radius of the electron's orbit is inversely proportional to its mass. In a universe with no Higgs field, a massless electron would have an infinite radius, meaning no atoms would form at all. In addition, differences in particle mass are also responsible for the decay of free neutrons to protons. This is called beta decay. Without the Higgs field, the universe may not have any protons at all. So this tiny 1 % mass contribution turns out to be responsible for 100 % of the universe we happen to have.

9th Class || Short Questions/Answers of chapter 8

Why metallic handle of a door is colder than the wood of the same door when touched?

Because, the transfer of heat from our hand to the metallic handle is faster, as compared to wood, thus loosing more thermal energy resulting in our hand feeling colder.

Which type of the clothes do the people of desert wear and why?

The people of the desert wear loose-fitting, long, heavy robes, and head wrappings. 

The loose-fitting cloth prevents sweat from evaporating quickly and allows the air to circulate, hence help the body to retain fluids. These clothes also protect people living in deserts from hot winds and dust storms.

Why does temperature of sea shore cities remain moderate during most of the year?does temperature of land areas vary more during winters and summers? Why

Water has a higher heat capacity than soil and rock, so the ocean takes much longer to heat and to cool than the land. Coastal areas will generally have more moderate temperatures than in land areas because of the heat capacity of the ocean. 

Warm ocean currents tend to raise winter temperatures, while cool currents can lower summer temperatures. Prevailing winds also affect world temperatures. The difference in temperature between the land and the sea in different seasons determines the temperature of the prevailing wind.

During the process of sweating (perspiration), we feel cooling during a hot day. Why? 

That's because cooling your body via sweating relies on a principle of physics called "heat of vaporization." It takes energy to evaporate sweat off of your skin, and that energy is heat. As your excess body heat is used to convert beads of sweat into vapor, you start to cool down.

How a bimetallic strip, made up of copper and iron is used as automatic switch in different devices? Give one example.

Thermal expansion of bimetallic strips used as a heat operated switch in the circuit of automatic equipment's like iron box, fire alarms, electric heater etc. Some thermometers work on the principle of expansion of liquids In automobile engines useful work is done by the expansion of gases. 

How is anomaly in the expansion of water help marine life to survive in extremely cold areas?

The anomalous expansion of water helps preserve aquatic life during very cold weather. When temperature falls, the top layer of water in a pond contracts, becomes denser and sinks to the bottom. A circulation is thus set up until the entire water in the pond reaches its maximum density at 4°C.

Examples of anomalous expansion of water

Bottle Burst: If you put a fully-filled water bottle in the refrigerator and its temperature is below 4 degrees Celsius, then according to the anomalous behavior of water, the water inside the bottle will expand. Therefore, due to no space in the bottle for the expansion of water molecules, water will exert force on the walls of the bottle and it will burst.

Breaking of Rocks: Rocks break during winter because as the temperature decreases below, water inside the rocks starts expanding and hence exert a large amount of force on the rocks and results in the breaking of rocks. 

Aquatic Life: This unique property of water helps aquatic life to survive. With a further drop in temperature, water on top forms ice and becomes a bad conductor of heat. This stops the heat from escaping the water body and helps aquatic life to survive. Hence, aquatic life can survive even when the temperature reaches or falls below. 

Why rollers are used at the ends of steel bridges?

One end of girder is fixed in concrete, but the other end is not fixed into concrete. It is supported on rollers. This is because when temperature increases in summer, the steel girder in a bridge expands and the rollers slide to allow the expansion otherwise the bridge may break. 

MCQs QUESTIONS Chapter 8

1. Temperature is equal to of substance.

A. Average K.E. of molecules

B. Individual K.E. of each molecule

C. Average P.E of molecules

D. Individual P.E. of each molecule

2. Boiling point of water is.

A. 212 °C

B. 212 °F

C. 100 K

D.373 °C

3. J/kg K is the unit of:

A. Specific Heat Capacity

B. Heat Capacity

C. Latent Heat of Fusion

D. Heat Energy

4. At temperature, water has maximum density?

A. 0 °C

B. -4 °C

C. -273 K

D. 4°C

5. Evaporation takes place from of liquid.

A. Surface

B. Bottom

C. center

D. any location

6. Number of divisions on Fahrenheit scale between its reference points are:

A. 100

B. 173

C. 212

D. 180

7. By adding heat at melting point, the temperature of substance does not change. Heat added to substance is used to of substance.

A. increase K.E. of particles

B. decrease K.E. of particles

C. increase the attraction between particles

D. decrease the attraction between particles

8. 336 J/g is latent heat of fusion of a material. How much heat is required to melt 10 g of material at its melting point?

A. 336J

B. 3360 J

C. 33600 J

D. 3.36× 1051

9. Substances with their specific heats are given below. Which of the following substances will cool down quickly if heated for same temperature?

A. Water (4200 J/kg K)

B. Wood (1700)/kg K)

C. Copper (400 J/kg K)

D. Silver (250)/kg K)

MULTIPLE CHOICE QUESTIONS || Thermal Properties of Matter

1. All the bodies expand on heating:

a) Variable

b) Constantly

c) Uniformly

d) All of them:

2. Temperature is the:

a) Mass contained by the body

b) Force of the molecules of body

c) Degree of hotness or coldness of the body 

d) none of above

3. The SI unit of temperature is:

a) °C

b) °F

c) K

d) °K

4. Temperature of 30 °C in Fahrenheit is:

a) 86 °F

b) 80 °F

c) 30 °F

d) 90 °F

5. Human normal body temperature of 37 °C in Fahrenheit is:

a) 98. 6 °F

b) 98 °F

c) 100 °F

d) None of above

6. Boiling point of water in Fahrenheit is:

a) 100 °F

b) 273 °F

c) 212 °F

d) 373 °F

7. Celsius equivalent of O K is:

a) -273 °C

b) -459.4 °C

c) 0 °C

d) 100 °C

8. Fahrenheit equivalent of OK is: 

a) -273 "F 

b) -459.4 °F

c) 0 °F

d) 100 °F

9. Heat is a type of energy: 

a) Kinetic

b) Potential 

c) Mechanical 

d) None of above

10. Linear expansion of a rod occur along- dimension(s):

a) One

b) Two

c) Three

d) All

11. The acteristic of unequal expansion of different metals is employed in a device known as:

a) Thermometer

b) Burner

c) Calorimeter

d) Thermostat

12. Linear expansion depends on:

a) Length of rod

b) Change in temperature 

c) Nature of material of rod

d) All of above

13. Thermostat works on the principle of: 

a) Unequal expansion of solids

c) Anomalous expansion of water

b) Pascal's law

d) Vaporization

Change of State

 Matter can be changed from one state to another. For such a change to occur, thermal energy is added to or removed from a substance.

Take a beaker and place it over a stand. Put small pieces of ice in the beaker and suspend a thermometer in the beaker to measure the temperature of ice. 

Now place a burner under the beaker. The ice will start melting. The temperature of the mixture containing ice and water will not increase above 0°C until all the ice melts and we get water at 0°C. If this water at 0°C is further heated, its temperature will begin to increase above 0 °C as shown by the graph in figure.

Part AB: On this portion of the curve, the temperature of ice increases from -30 °C to 0 °C.

Part BC: When the temperature of ice reaches 0 °C, the ice water mixture remains at this temperature until all the ice melts.

Part CD: The temperature of the substance gradually increases from 0 °C to 100 °C. The amount of energy so added is used up in increasing the temperature of water.

Part DE: At 100 °C water begins to boil and changes into steam. The temperature remains 100 °C till all the water changes into steam.

MDCAT Preparatory questions of Chapter 4 Work and Energy

A truck and a car are moving with equal velocity. On applying brakes, both will stop after a certain distance, then?

A. Truck will cover less distance before stopping 

B. Car will cover less distance before stopping

C. Both will cover equal distance

D. None of the mentioned 

What sort of energy does flying bird possess?

A. Potential energy

B. Kinetic energy

C. Both potential and kinetic energy 

D. Both potential and kinetic energy

When the velocity of an aero plane is doubled, the momentum

A. Remains unchanged 

B. Is conserved

C. Becomes zero

D. Increases uniformly

A machine gun fires 60 bullets per minute, with a velocity of 700m/s. If each bullet has a mass of 50g, find the power developed by the gun.

A. 1225W 

B. 12250W

C. 122.5W

D. 122W

A bullet fired from a gun can pierce a target due to its

A. Mechanical energy 

B. Heat energy

C. Kinetic energy

D. Acceleration

Kinetic energy with any reference must be

A. Zero

B. Positive

C. Negative

D. Either negative or positive 

At what angle work done will be maximum?

A. 0°

B. 45°

C. 90°

D. 30°

Which one of the following is a greater work? 

A. +100 J

B. -1000 J

C. -100 J

D. +200 J

Work done will be zero if angle between Force and displacement is:

A. 0°

B. 270°

C. 60°

D. 360°

A force 2i+j has moved its point of application from (2,3) to (6,5). What is work done?

A.-10

B.-18

C. +10

D. +18

At what angle the work done will be half of its maximum value

A. 0°

B. 300°

C. 45°

D. 60°

A man pushes a wall with 50 (N) and it displaces it zero (m), his work is

A. Negative

B. No work

C. Positive

D. May all possible

If a mass of 5 Kg is lifted upto 5m height, what will be the work done against the gravitational field

A. 245 J

B. 25 J

C. 49 J

D. 98 J

A person walks 2 m with an acceleration of 5 ms^-2, holding an object of mass 2 kg. The net work done on the object is

A. 20 J

B. 10 J

C. 5 J

D. 0 J

A force of 3i+2j+4k N gives displacement of 10j m. The work done is 

A. 20 J

B. 26 J

C. 32 J

D. Zero

A body travels displacement of 10 m by force of 5 N If work done is 25 J then angle between F and d is

A. 0°

B. 450°

C. 30°

D. 60°

A person holds a bucket of weight 60 N. He walks 7 m along the horizontal path and then climbs up a vertical distance of 5 m. The work done by the gravity is:

A. 300 N-m

B. 720 N-m

C. 420 N-m

D. None of these

If force and displacement of particle in direction of force are doubled. Work would be 

A. Double  

B. 1/4 times 

C. Half

D. 4 times

A person is holding a bucket by applying a force of 10N. He moves a horizontal distance of 5m and then climbs up a vertical distance of 10m. Find the total work done by him? 

A. 50J  

B. 100J 

C. 150J

D. 2003

A gardener pushes a lawn roller through a distance of 20m. If he applies a force of 20kg weight in a direction inclined at 60° to the ground, find the work done by him. (g = 9.8m/s²)

A. 400J

B. 250J

C. 1960J

D. 2514J

If velocity is double, then

A. Momentum increase 4 times and K.E increases 2 times

B. Momentum increases 2 times and K.E increase constant

C. Momentum and K.E remain same 

D. Momentum increases 2 times and K.E increases 4 times

What will be the ratio of kinetic energies of alpha particle and proton if their linear momentum will be same?

A. 18:1

B. 4:1

C. 1:4 

D. 104: 1

The Bodies of one kg and four kg have same kinetic energy. The ratio in their momenta will be

A. 1:2

B. 1:4

C. 1:16

D. 1:1

The velocity and momentum of a moving body are 10,000 cm-s^-1 and 10,000 g cm-s^-1 respectively. The K.E will be

A. 5 × 10s⁷ J

B. 5×10 J

C. 5 x 10s² J

D. 5X10° J

If momentum of a moving object is doubled then its kinetic energy will be

A. Doubled

B. Four times 

C. Halved

D. Same

The momentum and kinetic energy of a ball is numerically equal. The numerical value of velocity is

A. 1 m/s

B. 3 m/s

C. 2 m/s

D. 4 m/s

Kinetic energy of a body moving with speed of 10 ms^-1 is 30 J. If its speed becomes 30 m/s its K.E will be

A. 10 J

B. 90 J

C. 180 J

D. 270 J

Car X is traveling at half the speed of car Y. Car X has twice mass of car Y. Which statement is correct?

A. Car X has half the kinetic energy of car Y 

B. Car X has twice the kinetic energy of car Y

C. Car X has one quarter of the kinetic energy of car Y 

D. The two cars have the same kinetic energy

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of:

A. √2:1

B. 1:2

C. 1:4

D. 1:√2

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s'. The K.E of other mass is

A. 324 J 

B. 256 J 

C. 486 J

D. 524 J

The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to

A. m⁰ 

B. m

C. m²

D. m^1/2

When force and displacement are in the same direction, the kinetic energy of the body 

A. Increases

B. Remains constant

C. Decreases

D. Becomes zero

A truck and a car are moving with equal velocity. On applying brakes, both will stop after a certain distance, then?

A. Truck will cover less distance before stopping 

B. Both will cover equal distance

C. Car will cover less distance before stopping

D. None of the mentioned

Potential energy per unit volume is given by

A. mgh 

B. gh

C. mgh/ρ

D. ρgh 

A body is falling from a height h. After it has fallen a height h/2, it will possess

A. Only potential energy 

B. Half potential and half kinetic energy 

C. Only kinetic energy

D. More kinetic and less potential energy

Energy stored in the spring of watch is

A. Electrical energy

B. potential energy

C. Kinetic energy

D. Elastic potential energy

A stone is thrown up from the surface of earth when it reaches at maximum height. Its total energy is equal to

A. mgh

B. 1/2mv²

C. Zero

D. 2 mgh

Energy consumed by 60-watt bulb in 2 minutes is equal to

A. 7.2 kilo joules

B. 120 joules

C. 720

 D. 72000 joules

The consumption of energy by 60-watt bulb in 2 seconds is:

A. 201

C. 120 J

B. 30J

D. 0.02 J

RESISTIVITY AND ITS DEPENDENCE UPON TEMPERATURE

It has been experimentally seen that the resistance R of a wire is directly proportional to its length L and inversely proportional to its cross sectional area A. Expressing mathematically we have

R ∝ L 

And 

R ∝ 1/A 

Or 

R ∝ L/A 

R = ρ L/A ....... (1)

where ρ is a constant of proportionality known as resistivity of specific resistance of the material of the wire. It may be noted that resistance is the characteristic of a particular wire whereas the resistivity is the property of the material of which the wire is made. From Eq. 1 we have

ρ = RA/L

The above equation gives the definition of resistivity as the resistance of a metre cube of a material. The SI unit of resistivity is (Ωm).

Conductance is another quantity used to describe the electrical properties of materials. In fact conductance is the reciprocal of resistance i.e.,

Conductance = 1 / resistance (R)

The SI unit of conductance is mho or siemen.

Likewise conductivity, σ is the reciprocal of resistivity i.e., 

σ = 1/ρ

The SI unit of conductivity is ohm^-1m^-1 or mho m^-1. Resistivity of various materials are given in Table.

It may be noted from Table that silver and copper are two best conductors. That is the reason that most electric wires are made of copper.

The resistivity of a substance depends upon the temperature also. It can be explained by recalling that the resistance offered by a conductor to the flow of electric current is due to collisions, which the free electrons encounter with atoms of the lattice. As the temperature of the conductor rises, the amplitude of vibration of the atoms in the lattice increases and hence, the probability of their collision with free electrons also increases. One may say that the atoms then offer a bigger target, that is, the collision cross-section of the atoms increases with temperature. This makes the collisions between free electrons and the atoms in the lattice more frequent and hence, the resistance of the conductor increases.

Experimentally the change in resistance of a metallic conductor with temperature is found to be nearly linear over a considerable range of temperature above and below 0 °C. Over such a range the fractional change in resistance per kelvin is known as the temperature coefficient of resistance i.e..

 α = (R_t - R₀)/R₀t

where R₀, and R_t, are resistances at temperature 0 °C and t°C. As resistivity ρ depends upon the temperature, Eq. gives 

R=ρ₀ L/A and R=ρ_t L/A

Substituting the values of R₀, and R_t, in Eq. we get

α = (ρ_t - ρ₀)/ρ₀t

where ρ₀ is the resistivity of a conductor at 0 °C and ρ_t is the resistivity at t °C. 

There are some substances like germanium, silicon etc; whose resistance decreases with increase in temperature. i.e;  these substances have negative temperature coefficients.

OHM'S LAW

We have seen that when a battery is connected across a conductor, an electric current begins. 

How much current flows through the conductor when a certain potential difference is set up across its ends? 

The answer to this question was given by a German Physicist George Simon Ohm. 

He showed by elaborate experiments that the current through a metallic conductor is directly proportional to the potential difference across its ends. This fact is known as Ohms' law which states that

"The current flowing through a conductor is directly proportional to the potential difference across its ends provided the physical state such as temperature etc of the conductor remains constant."

Symbolically Ohm's law can be written as

Ι ∝ ν

It implies that

V=RI

where R, the constant of proportionality is called the resistance of the conductor. 

The value of the resistance depends upon the nature, dimensions and the physical state of the conductor.  

Define resistance.

The resistance is a measure of the opposition to the motion of electrons due to their continuous bumping with the atoms of the lattice. 

Unit of resistance.

The unit of resistance is ohm. 

One ohm.

A conductor has a resistance of 1 ohm if a current of 1 ampere flows through it when a potential difference of 1 volt is applied across its ends. 

The symbol of ohm is Ω. 

If I is measured in amperes, V in volts, then R is measured in ohms i.e.

R(ohms)=V (volts)/I (amperes)

Ohmic Conductors

A sample of a conductor is said to obey Ohm's law if its resistance R remains constant that is, the graph of its V versus I is exactly a straight line. A conductor which strictly obeys Ohm's law is called ohmic. 

Non Ohmic Conductors

There are devices, which do not obey Ohms' law i.e., they are non ohmic. The examples of non ohmic devices are filament bulbs and semiconductor diodes.

Let us apply a certain potential difference across the terminals of a filament lamp and measure the resulting current passing through it. If we repeat the measurement for different values of potential difference and draw a graph of voltage V versus current 7, it will be seen that the graph is not a straight line. It means that a filament is a non ohmic device. This deviation of I-V graph from straight line is due to the increase in the resistance of the filament with temperature.

As the current passing through the filament is increased from zero, the graph is a straight line in the initial stage because the change in the resistance of the filament with temperature due to small current is not appreciable. As the current is further increased, the resistance of the filament continues to increase due to rise in its temperature.

Another example of non ohmic device is a semiconductor diode. The current - voltage plot of such a diode is shown in Figure. The graph is not a straight line so semi conductor is also a non ohmic device.

Review of Series and Parallel Combinations of Resistors

In an electrical circuit, usually, a number of resistors are connected together. There are two arrangements in which resistors can be connected with each other., one is known as series arrangement and other one as parallel arrangement.

Series Combination of resistance 

If the resistors are connected end to end such that the same current passes through all of them, they are said to be connected in series as shown in Figure. There equivalent resistance R, is given by

R_eq=R₁+R₂+R₃+------

Parallel combination of resistance 

In parallel arrangement a number of resistors are. connected side by side with their ends joined together at two common points as shown. in Figure. The equivalent resistance R. of this arrangement is given by 

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃+..........

EFFECTS OF CURRENT

The presence of electric current can be detected by the various effects which it produces. The obvious effects of the current are:

(i) Heating effect

(ii) Magnetic effect

(iii) Chemical effect 

Heating Effect

Current flows through a metallic wire due to motion of free electrons. During the course of their motion, they collide frequently with the atoms of the metal. At each collision, they lose some of their kinetic energy and give it to atoms with which they collide. Thus as the current flows through the wire, it increases the kinetic energy of the vibrations of the metal atoms. i.e., it generates heat in the wire. It is found that the heat H produced by a current / in the wire of resistance R during a time interval tis given by

H=I²Rt

The heating effect of current is utilized in electric heaters, kettles, toasters and electric irons etc. 

Magnetic Effect

The passage of current is always accompanied by a magnetic field in the surrounding space. The strength of the field depends upon the value of current and the distance from the current element. The pattern of the field produced by a current carrying straight wire, a coil and a solenoid is shown in Figure. Magnetic effect is utilized in the detection and measurement of current. All the machines involving electric motors also use the magnetic effect of current.

Chemical Effect

Certain liquids such as dilute sulphuric acid or copper sulphate solution conduct electricity due to some chemical reactions that take place within them. The study of this process is known as electrolysis. The chemical changes produced during the electrolysis of a liquid are due to chemical effects of the current. It depends upon the nature of the liquid and the quantity of electricity passed through the liquid. 

The liquid which conducts current is known as electrolyte. The material in the form of wire or rod or plate which leads the current into or out of the electrolyte is known as electrode. The electrode connected with the positive terminal of the current source is called anode and that connected with negative terminal is known as cathode. The vessel containing the two electrodes and the liquid is known as voltameter. As an example we will consider the electrolysis of copper sulphate solution. The voltameter contains dilute solution of copper sulphate. The anode and cathode are both copper plates. 

When copper sulphate is dissolved in water, it dissociates into Cu⁺⁺ and SO₄^--, ions. On passing current through the voltameter. Cu moves towards the cathode and the following reaction takes place.

Cu⁺⁺+2e^-- -------> Cu 

The copper atoms9 thus formed are deposited at cathode plate. While copper is being deposited at the cathode, the SO, ions move towards the anode. Copper atoms from the anode go into the solution as copper ions which combine with sulphate ions to form copper sulphate. 

Cu+SO -----> CuSO

As the electrolysis proceeds, copper is continuously deposited on the cathode-while an equal amount of copper from the anode is dissolved into the solution and the density of copper sulphate solution remains unaltered.

This example also illustrates the basic principle of electroplating a process of coating a thin layer of some expensive metal (gold, silver etc.) on an article of some cheap metal.

SOURCE OF CURRENT

When two conductors at different potentials are joined by a metallic wire, current will flow through the wire. The current continues to flow from higher potential to the lower potential until both are at the same potential. After this the current ceases to flow. Thus the current through the wire decreases from a maximum value to zero. In order to have a constant current the potential difference across the conductors or the ends of the wire should be maintained constant. This is achieved by connecting the ends of the wire to the terminals of a device called a source of current.

Every source of current converts some non electrical energy such as chemical, mechanical, heat or solar energy into electrical energy. There are many types of sources of current. A few examples are mentioned below:

(1) Cells (primary as well as secondary) which convert chemical energy into electrical energy.

(ii) Electric generators which convert mechanical energy into electrical energy.

(iii) Thermo-couples which convert heat energy into electrical energy.

(iv) Solar cells which convert sunlight directly into electrical energy. 

ELECTRIC CURRENT

An electric current is caused by the motion of electric charge. 

If a net charge ∆Q passes through any cross section of a conductor in time ∆t, we say that an electric current I has been established through the conductor where 

   I = ∆Q/∆t

The SI unit of current is ampere and it is a current due to flow of charge at the rate of one coulomb per second.

Motion of electric charge which causes an electric current is due to the flow of charge carriers. 

• In case of metallic conductors, the charge carriers are electrons. 
• The charge carriers in electrolyte are positive and negative ions.
• In gases, the charge carriers are electrons and ions.

Current Direction

History: Early scientists regarded an electric current as a flow of positive charge from positive to negative terminal of the battery through an external circuit. 

Later on, it was found that a current in metallic conductors is actually due to the flow of negative charge carriers called electrons moving in the opposite direction i.e., from negative to positive terminal of the battery, but it is a convention to take the direction of current as the direction in which positive charges flow. 

This current is referred as conventional current. The reason is that it has been found experimentally that positive charge moving in one direction is equivalent in all external effects to a negative charge moving in the opposite direction. 

As the current is measured by its external effects so a current due to motion of negative charges, after reversing its direction of flow can be substituted by an equivalent current due to flow of positive charges.

Conventional Current 

"The conventional current in a circuit is defined as that equivalent current which passes from a point at higher potential to a point at a lower potential as if it represented a movement of positive charges."

While analyzing the electric circuit, we use the direction of the current according to the above mentioned convention. 

If we wish to refer to the motion of electrons, we use the term electronic current. 

Current Through a Metallic Conductor

In a metal, the valence electrons are not attached to individual atoms but are free to move about within the body. These electrons are known as free electrons. The free electrons are in random motion just like the molecules of a gas in a container and they act as charge carriers in metals. The speed of randomly moving electrons depends upon temperature.

If we consider any section of metallic wire, the rate at which the free electrons pass through it from right to left is the same as the rate at which they pass from left to right. As a result the current through the wire is zero. 

If the ends of the wire are connected to a battery, an electric field E will be set up at every point within the wire. The free electrons will now experience a force in the direction opposite to E. As a result of this force the free electrons acquire a motion in the direction of -E. It may be noted that the force experienced by the free electrons does not produce a net acceleration because the electrons keep on colliding with the atoms of the conductor. The overall effect of these collisions is to transfer the energy of accelerating electrons to the lattice with the result that the electrons acquire an average velocity, called the drift velocity in the direction of -E. 

The drift velocity is of the order of 10^-3 ms^-1, whereas the velocity of free electrons at room temperature due to their thermal motion is several hundred kilometres per second.

Thus, when an electric field is established in a conductor, the free electrons modify their random motion in such a way that they drift slowly in a direction opposite to the field. In other words the electrons, in addition to their violent thermal motion, acquire a constant drift velocity due to which a net directed motion of charges takes place along the wire and a current begins to flow through it. 

Steady Current

A steady current is established in a wire when a constant potential difference is maintained across it which generates the requisite electric field E along the wire.

Electric Charge

Electric Charge is the Intrinsic property of fundamental particles (like electrons, w bosons and quarks etc).

OR

 Electric charge is the intrinsic physical property of matter that causes it to experience a force when kept in an electric or magnetic field. 

An electric charge is associated with an electric field, and the moving electric charge generates a magnetic field. A combination of electric and magnetic fields is known as the electromagnetic field. 

Electrostatics

• The study of charges at rest is called electrostatics.
• The fundamental law of electrostatics is called Coulomb's law.

Current and Electricity 

• The study of charges with constant speed is called current and electricity.
• The fundamental law of current and electricity is Ohm's law. 

Electricity and Magnetism 

• The study of charges with variable speed is called electricity and magnetism. 
• The fundamental laws of electricity and magnetism are Maxwell Equations.

ELECTRIC FIELD

 Transmission of Electric Field 

To describe the mechanism by which electric force is transmitted, Michael Faraday (1791-1867) introduced the concept of an electric field. According to his theory, it is the intrinsic property of nature that an electric field exists in the space around an electric charge. 

Force Field

The electric field is considered to be a force field that exerts a force on other charges placed in that field. For example, a charge q produces an electric field in the space surrounding it. This field exists whether the other charges are present in space or not. 

Presence of Electric Field 

The presence of field cannot be tested until another charge q0, is brought into the field. Thus the field of charge q interacts with q0, to produce an electrical force. The interaction between q and q0, is accomplished in two steps: 

(a) the charge q produces a field 

(b) the field interacts with charge q0, to produce a force F on q. 

These two steps are illustrated in Figure.

In this figure the density of dots is proportional to the strength of the field at the various points. We may define electric field strength or electric field intensity E at any point in the field as where F is the force experienced by a positive test charge q. placed at the point. The test charge q0, has to be very small so that it may not distort the field which it has to measure.

E = F/q0 ......... (1)

Since electric field intensity is force per unit charge, it is measured in newton per coulomb in SI units. It is a vector quantity and its direction is the same as that of the force F.

Place a positive test charge q0, at this point. The Coulomb's force that this charge will experience due to q is

where r is a unit vector directed from the point charge q to the test point where q0, has been placed, i.e., the point where the electric intensity is to be evaluated. By Eq.

THE EXPANSION OF THE UNIVERSE

The evidence for the expansion of the universe comes from the change in wavelength of the light emitted by distant galaxies. We analyzed a similar effect as the relativistic Doppler shift, which we can write in terms of wavelength as

..... 1

where v represents the relative velocity between the source of the light and the observer. Here λ' is the wavelength we measure on Earth and λ* is the wave length emitted by the moving star or galaxy in its own rest frame.

The light emitted by a star such as the Sun has a continuous spectrum. As light passes through the star's atmosphere, some of it is absorbed by the gases in the atmosphere, so the continuous emission spectrum has a few dark absorp tion lines superimposed. Comparison between the known wavelengths of these lines (measured on Earth for sources at rest relative to the observer) and the Doppler-shifted wavelengths allows the speed of the star to be deduced from Equation 1.

      Of the stars in our galaxy, some are found to be moving toward us, with their light shifted toward the shorter wavelengths (blue), and others are mov ing away from us, with their light shifted toward the longer wavelengths (red). 

The average speed of these stars relative to us is about 30 km/s (10^-4 c). The change in wavelength for these stars is very small. Light from nearby galaxies, those of our "local" group, again shows either small blue shifts or small red shifts.

However, when we look at the light from distant galaxies, we find it to be systematically red shifted, and by a large amount. Some examples of these measurements are shown in Figure . We do not see a comparable num ber of red and blue shifts, as we would expect if the galaxies were in random motion. All of the galaxies beyond our local group seem to be moving away from us.

The cosmological principle asserts that the universe must look the same from any vantage point, and so we must conclude that any other observer in the universe would draw the same conclusion: The galaxies would be observed to recede from every point in the universe.

Hubble's Law

In the 1920s, astronomer Edwin Hubble was using the 100-inch telescope on Mount Wilson in California to study the wispy nebulae. By resolving indi vidual stars in the nebulae, Hubble was able to show that they are galaxies like the Milky Way, composed of hundreds of billions of stars. Hubble also was able to observe variable stars in the distant galaxies whose brightness oscillated with periods of days. Using a scale of period vs. brightness for the variable stars in nearby galaxies developed in 1908 by astronomer Henrietta Swan Leavitt, Hubble deduced the distances to the remote galaxies. Finally, plotting his deduced distances against the recessional velocities obtained from the red shifts, Hubble established the empirical relationship between distance and speed known as Hubble's law:

v = H_o d

The proportionality constant H0 is known as the Hubble parameter.

Figure a shows a plot of Hubble's data. Although the points scatter quite a bit (due primarily to uncertainties in the distance measurements), there is a definite indication of a linear relationship. (Hubble's distance calibra tion was incorrect, so the labels on the horizontal axis do not correspond to the actual distances to the galaxies.) 

More modern data based on observing supernovas in distant galaxies are shown in Figure b. There is again clear evidence for a linear relationship, and the slope of the line gives a value of the Hubble parameter of about 72 km/s/Mpc*, within a range of about ±10%. The Hubble parameter can also be determined from a variety of other cosmo logical experiments. These agree with the supernova data, and the best current value is 

The uncertainty in this value is on the order of +4%.

*A parsec, pc, is a measure of distance on the cosmic scale; it is the distance that corresponds to one angular second of parallax. Because parallax is due to the Earth's motion around the Sun, the parallax angle 2a is the diameter 2R of the Earth's orbit divided by the distance d to the star or galaxy. Thus, a = R/d radians, which gives 1 pc = 3.26 light-years = 3.084 x 10¹³ km. One megaparsec, Mpc, is 10⁶ pc. 

The Hubble parameter has the dimension of inverse time. As we show later, H0^-1 is a rough measure of the age of the universe. The best value of Ho gives an age of 14 x 10⁹ y. If the speed of recession has been changing, the true age can be less than H¹.

How does the Hubble law show that the universe is expanding? 

Consider the unusual universe represented by the three-dimensional coordinate system shown in Figure a, where each point represents a galaxy. With the Earth at the origin, we can determine the distance d to each galaxy. If this universe were to expand, with all the points becoming farther apart, as in Figure b, the distance to each galaxy would be increased to d'. Suppose the expansion were such that every dimension increased by a constant ratio k in a time t; that is, x' = kx, and so forth. Then d' = kd, and a given galaxy moves away from us by a distance d'-d in a time t, so its apparent recessional speed is 

If we compare two galaxies 1 and 2,

a relationship identical with Hubble's law, Eq. Thus, in an expanding universe, it is perfectly natural that the farther away from us a galaxy might be, the faster we observe it to be receding.

Notice also from Figure a that this is true no matter which point we hap pen to choose as our origin. From any point in the "universe" of Figure 15.3, the other points would be observed to satisfy Eq. 15.4 and thus also Hubble's law. We can further demonstrate this with two analogies. 

If we glue some spots to a balloon and then inflate it, every spot observes all other spots to be moving away from it, and the farther away a spot is from any point, the faster its separation grows. 

For a three-dimensional analogy, consider the loaf of raisin bread shown in Figure  rising in an oven. As the bread rises, every raisin observes all the others to be moving away from it, and the speed of recession increases with the separation.

The correct interpretation of the cosmological redshifts requires the tech niques of general relativity, which we discuss later in this chapter. According to general relativity, the shift in wavelength is caused by a stretching of the entire fabric of spacetime. Imagine small photos of galaxies glued to a rubber sheet. As the sheet is stretched, the distance between the galaxies increases, but they are not "in motion" according to the terms we usually use in physics to describe motion. However, the stretching of the space between the galaxies causes the wavelength of a light signal from one galaxy to increase by the total amount of the stretching before it is received at another galaxy. This is very different from the usual interpretation of the Doppler formula (Eq). (In fact, for some galaxies the wavelength shift is so large that the special relativ ity formula would imply a recessional speed greater than the speed of light!) At low speeds, the Doppler interpretation of the redshift (that is, calculat ing a speed from the Doppler formula and using that speed in Hubble's law) gives results that correspond with those based on an expansion of spacetime. 

However, for very large cosmological redshifts, a more correct analysis must be based on the stretching model:

where Ro represents a "size" or distance scale factor of the universe at the present time and R represents a similar factor at the time the light was emitted.

The expansion of the universe has been widely accepted since Hubble's discoveries in the 1920s. There are, however, two interpretations of this expan sion. (1) If the galaxies are separating, long ago they must have been closer together. The universe was much denser in its past history, and if we look back far enough we find a single point of infinite density. This is the "Big Bang" hypothesis, developed in 1948 by George Gamow and his colleagues. (2) The universe has always had about the same density it does now. As the galaxies separate, additional matter is continuously created in the empty space between the galaxies, to keep the density more or less constant. This is the "Steady State" hypothesis, proposed also in 1948 by astronomer Fred Hoyle and others. New galaxies created from this new matter would make the uni verse look the same not only from all vantage points but also at all times in the present and future. (To keep the density constant, the rate of creation need be only about one hydrogen atom per cubic meter every billion years.)

Both hypotheses had their supporters, and during the 1940s and 1950s, the experimental evidence did not seem to favor either one over the other. In the 1960s, the new field of radio astronomy revealed the presence of a universal background radiation in the microwave region, which is believed to be the remnant radiation from the Big Bang. This single observation has propelled the Big Bang theory to the forefront of cosmological models.

Baryons

 

Baryons are strongly interacting particles having half-integral spins (1/2, 3/2, 5/2 . . . . .). A partial listing of some baryons is given in Table. The familiar members of the baryon family are the proton and neutron. Baryons have distinct antiparticles for example, the antiproton (p) and antineutron (n).

Some selected mesons

Particle	Antiparticle	Charge	Spin (h/2π)	Strangeness	Rest Energy (MeV)	Mean Life (s)	Typical Decay Products
p		+1	½	0	938	ꝏ
n		0	½	0	940	887	p + e- + e
A0		0	½	-1	1116	2.6 x10-10	p + π-
Σ+		+1	½	-1	1189	0.8x10-10	p + π0
Σ0		0	½	-1	1193	7.4x10-20	A0 + ϒ
Σ -		-1	½	-1	1197	1.5x10-10	n + π-
Ξ0		0	½	-2	1315	2.9x10-10	A0 + π0
Ξ-		-1	½	-2	1321	1.6x10-10	A0 + π-
∆*		+2,+1 0,-1	3/2	0	1232	5.9x10-24	p + π
Σ*		+1,0,-1	3/2	-1	1385	1.8x10-23	A0 + π
Ξ*	---	-1, 0	3/2	-2	1530	7.3x10-23	Ξ + π
Ω-	---	-1	3/2	-3	1672	8.2x10-11	A0 +K-
Ae+	---	+1	½	0	2285	2.1x10-13	p +K- + π+
Ab0	---	0	½	0	5624	1.2x10-12	p +D0 + π-

We can produce heavier baryons in reactions between nucleons, such as 

p + p——> p +A^o  + K⁺,

which produces the A^o baryon and the K⁺ meson. The A^o decays according to

A^o ——> p + π^-          (mean life = 2.6 X 107" s).

Although there are no neutrinos produced in the decay, the

mean life indicates that the decay is governed by the weak

interaction.