### Welcome to Talha's Physics Academy

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Talha's Physics Academy is an exploration environment for concepts in physics which employs free Physics Books and other linking strategies to facilitate smooth navigationThe entire environment is interconnected with thousands of links, reminiscent of a neural network.

New content for Talha's Physics Academy will be posted as it is developed,It is my intent to keep this material continuously available except for brief maintenance times.

All the Branches of Physics are covered.

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### Electromagnetic Induction:C.R.Q's /Questions

15.1 Does the induced emf in a circuit depend on the resistance of the circuit?does the induced current depend on the resistance of the circuit?

Ans. The Induced emf in a coil depends upon the rate of change of flux through it (E=-Nt) .Hence its value does not depend upon the resistance of the coil.But the induced current that flows through a coil is equal to I=E/R and it’s value depends on the resistance of the coil.If , resistance increases then the current flowing through the coil decreases.Because the product of I and R must remains constant.i.e. I x R = Constant.

15.2 A square loop of wire i moving through a uniform magnetic field.The normal to the loop is oriented parallel to the magnetic field.Is emf induced in th loop?Give a reason for your answer.

Ans.No, induced emf will not be produced because there is no change of flux linking to the loop.i.e.t=0 .So according to the relation (E=-Nt) ,E=0.If the square loop is being rotated in magnetic field in such a way that the loop is cutting the magnetic field lines due to its motion,then emf will induce in the coil.

15.3 A light metallic ring is released from above into a vertical bar magnet.Viewed for above ,does the current flow clockwise or anticlockwise in the ring?

Ans.According to Faraday’s law of electromagnetic induction an induced emf and hence induced current will be produced in the metallic ring.According to Lenz law , the current in the ring should flow in such a direction as to oppose the cause producing it.So, the induced current in the coil must produce magnetic field which opposes the motion of ring towards bar magnet.The side of the ring facing magnet will be North Pole of the induced magnetic field.Right hand rule shows that the magnetic field will produce in this manner only when the current will flow in clockwise direction in ring.

15.4 What is the direction of the current through resistor R in the figure.When switch S is (a) closed (b) opened.

Ans.(a) When the switch is closed ,the current in the coil increases from zero to maximum steady value;during during this interval magnetic flux in the second coil from zero to max. and induced current will flow in it.The side of the current carrying coil facing the other coil becomes North pole.So,to oppose N pole , the current in the other coil must flow anti clockwise.Hence current in R flow from left to right according to the figure.

(b) however, when the switch is opened, the current in the coil decreases from max. to zero and flux linked to the other coil also decreases and induced current is produced in the reverse direction.So, the current will flow from Right to Left (clockwise) according to the figure.

15.5 Does the induced emf always act to decrease the magnetic flux through a circuit?

Ans.No, the induced emf does not act as to decrease magnetic flux through a circuit.According to Lenz law , the current in the ring should flow in such a direction as to oppose the cause producing it.If an induced emf appears in a circuit  due to decreasing magnetic flux linking that circuit then induced current flowing through the circuit will produce its own magnetic field that oppose the decrease of the magnetic field.In other word it is increasing the magnetic flux through a circuit.

15.6 When the switch in the circuit is closed a current is established in the coil and the metal ring jumps upward.Why?Describe what would happen to the ring is battery polarity were reversed?

Ans.From establishment of current, induced magnetic flux will be produced in the  cylinder. From Lenz’s law an opposing emf in the ring will be produced. The face of the ring opposite to coil develops similar pole of magnet and experiences repulsion, which makes it to jump upward.
The ring will jump upward in the same manner, if the battery polarity is reversed. The same process will happen as mentioned above.

15.7 The Fig. Shows a coil of wire in the xy plane with a magnetic field directed along the y- axis. Around which of the three coordinate axes should the coil be rotated in order to generate an emf and a current in the coil?

Ans.The coil must be rotated about x-axis to get change of magnetic flux and induced current through it.

15.8 How would you position a flat loop of wire in a changing magnetic field so that there
is no emf induced in the loop?

Ans.If the flat loop of wire is parallel to the field. When the coil is held parallel to the direction of B, then the angle between vector area A and B will be 90o
.
φB = B•A = BAcos90o= 0

15.9 In a certain region the earth’s magnetic field point vertically down. When a plane flies due north, which wingtip is positively charged?

Ans.[At the two magnetic poles, the direction of the earth’s magnetic field is vertical. At north magnetic pole it is downward into the ground, at south magnetic pole, it is upward out of the ground. Here on both places, the compass needle does not indicate any particular direction along the ground.]
Left wingtip will be positively charged. The electrons in the wing experience the magnetic force [ F = -e(vxB)] From R.H. rule, the electrons will move towards right, (the direction of conventional current is left). Due to it left wingtip (West side) will be positively charged.

15.10 Show that ε and ∆Φ / ∆t have the same units.

Ans.
15.11 When an electric motor, such as an electric drill, is being used, does it also act as a
generator? If so what is the consequences of this?

Ans.Yes it also acts as a generator. When the electric motor is running, due to rotation of its coil, an emf is induced in it. It is called back emf, which produces opposing current. It increases with speed of motor. This means that it also acts as a generator.

15.12 Can a D.C. motor be turned into a D.C. generator? What changes required to be done?

Ans. Yes a d.c. motor can be turned into a d.c. generator.To change it, needs some arrangement to rotate the armature. Disconnect the brushes of the commutator from d. c. supply and connect it with some external circuit.

15.13 Is it possible to change both the area of the loop and the magnetic field passing
through the loop and still not have an induced emf in the loop?

Ans. Yes, if the flux remains constant. From the equation; ∆φ = B•A ,B and A are inversely proportional to each other. If the area of the loop and magnetic field passing through the loop are changed in such a way to make product constant, then no induced emf will be produced.
Secondly, if plane of the coil is parallel to the magnetic field, changing in area and the field will not induce any emf in the loop.

15.14 Can an electric motor be used to drive an electric generator with the output from the generator being used to operate the motor?

Ans. No. An electric motor cannot be used to drive an electric generator. Perpetual
motion machine is not possible according to law of conservation of energy.

15.15 A suspended magnet is oscillating freely in horizontal plane. Oscillations are strongly damped when a metal plate is placed under the magnet. Explain why this occurs?

Ans. The metal plate produces an induced emf, due to oscillations in the suspended magnet.This induced emf produces current, which produces its own magnetic field that will oppose the motion of the suspended magnet. So oscillations are strongly damped.

Q.16 Four unmarked wires emerge from a transformer. What steps would you take to
determine the turns ratio?

Ans. Separate primary and secondary coils by ohmmeter. Connect primary coil with a.c. supply of known voltage Vp . measure the voltage induced Vs by voltmeter. Calculate turns ratio from; Vs / Vp = Ns / Np

15.17 a) Can a step-up transformer increase the power level? b) In a transformer, there is no transfer of charge from the primary to the secondary. How is, then the power transferred?

Ans. a) No. A step up transformer cannot increase the power level. As for ideal
case : power input = power out .It can increase or decrease voltage or current but power, P = VI, will remain same.
b) Due to induced emf, power is transferred. There is no transfer of charge, but the change of flux in one coil is linked with the other coil and emf is produced.

15.18 When the primary of a transformer is connected to a.c. mains the current in it
a) is very small if the secondary circuit is open, but
b) increases when the secondary circuit is closed. Explain these facts.

Ans. a) The output power is zero, if the secondary circuit is open, very small current is drawn by the primary coil from a.c. mains.
b) Output power will increase, when the secondary circuit is closed.
Power input = Power output , Greater current is needed in primary for equalizing power in the secondary coil.

### What is Non Newtonian Fluid?

Many people have heard of Sir Isaac Newton. He is famous for developing many scientific theories in mathematics and physics. Newton described how ‘normal’ liquids or fluids behave, and he observed that they have a constant viscosity (flow). This means that their flow behaviour or viscosity only changes with changes in temperature or pressure. For example, water freezes and turns into a solid at 0˚C and turns into a gas at 100˚C. Within this temperature range, water behaves like a ‘normal’ liquid with constant viscosity.

Typically, liquids take on the shape of the container they are poured into. We call these ‘normal liquids’ Newtonian fluids. But some fluids don’t follow this rule. We call these ‘strange liquids’ non-Newtonian fluids.

Stress and strain

In science, stress means that a force is applied to a body. The result of that stress is described as strain.

Imagine hitting a metal with a hammer. The force that is applied on the metal causes stress to that particular area. The result of that stress is then described as strain – in this case, possibly a deformation of the metal. Newtonian fluids don’t resist much stress that is applied on them like solids would do, so they don’t show the signs of strain. If you hit water with a hammer, the liquid will not resist much to the stress applied and will also not show signs of strain.

Thixotropic and rheopectic are non-Newtonian liquids that react as a result of the length of time that stress is applied.

Non-Newtonian fluids change their viscosity or flow behaviour under stress. If you apply a force to such fluids (say you hit, shake or jump on them), the sudden application of stress can cause them to get thicker and act like a solid, or in some cases it results in the opposite behaviour and they may get runnier than they were before. Remove the stress (let them sit still or only move them slowly) and they will return to their earlier state.

Say you want to get some tomato sauce out of the bottle. You know there is some in there, but when you turn the bottle upside down, nothing comes out. So what do you do? You shake or hit the bottle. This causes the tomato sauce to become more liquid and you can easily squirt some out. In this case, the sauce’s viscosity decreases and it gets runnier with applied stress.

Oobleck is a mixture of cornflour and water (similar to uncooked custard) named after a substance in a Dr Seuss book. This liquid is a runny goo until you apply stress to it, and then it suddenly acts like a solid. You can hit a bowlful with a hammer, and instead of splashing everywhere, the particles lock together. You can roll it into a solid ball in your hand, but if you stop moving it, it reverts to liquid and oozes out through your fingers. In this case, the oobleck’s viscosity or resistance to flow increases with applied stress.

Different types of non-Newtonian fluids

Not all non-Newtonian Fluids behave in the same way when stress is applied – some become more solid, others more fluid. Some non-Newtonian fluids react as a result of the amount of stress applied, while others react as a result of the length of time that stress is applied.

Why do non-Newtonian fluids matter?

The behavior of non-Newtonian fluids has important implications:

If a house is built on certain types of clay and an earthquake puts stress on this material through the sudden movement, the apparently solid clay can turn into a runny liquid.
Body armor that behaves like a liquid so that you can move easily but turns into a solid on impact from stress could be useful for police or the military.
Fun! Making oobleck is a great reason to make a mess, all in the name of science!

### The ratio of the dimensions of G to those of g is..... ?

The dimension of G can be found by the formula F=Gm1m2/r2
i.e. G=F r2/ m1m2
Dimensions: [F]=MLT-2         [r]=L               [m]=M
So [G] = MLT-2 L2M-2=M-1L3T-2
Now, the dimension of g is given by
[g]=LT-1
Now, finding the ratio of G to g;
ð M-1L3T-2/ LT-1
ð M-1 L2 T-1

Hence it is the ratio of dimensions of G to the dimensions of g.

### Types Of Galaxies

Many different types of galaxies exist. The different types of galaxies not only appear different, but have different evolutionary histories as well. The three fundamental classes of galaxies are elliptical, spiral, and irregular. These categories are further broken down into subclasses, often illustrated using a Hubble tuning fork diagram. Originally, scientists thought this diagram may have represented an evolutionary sequence for galaxies, but today we know that this is not true. The formation and evolution of galaxies is a complex process that is poorly understood.

### Ellipticals

Elliptical galaxies are so named because they have elliptical shapes: they look like fat, fuzzy eggs or footballs. Stars in ellipticals do not spread out into a thin disk, as they do in spiral galaxies; instead, they wrap evenly around the galaxy's center in all directions. Ellipticals have smoothly varying brightnesses, with the degree of brightness steadily decreasing outward from the center. If you look at an ellipse-shaped surface that surrounds the center of an elliptical, all the stars on that surface will have similar brightnesses. Elliptical galaxies are also nearly all the same color: somewhat redder than the Sun. On the tuning fork diagram, they are classified as E, followed by a number indicating how elliptical a given galaxy is. The higher the number, the more elliptical the galaxy; that is, the longer the galaxy is with respect to its width.

The reddish color of ellipticals (as well as other more detailed observations) tells us something important their histories. The galaxies' red color comes from older, cooler stars. The fact that most of the light comes from old stars suggests that most ellipticals formed long ago. The fact that the color of an elliptical is more or less the same throughout the galaxy suggests that most of the stars in these galaxies formed at about the same time.

In addition, most elliptical galaxies in the universe are found near other elliptical galaxies, in galaxy clusters. In these clusters, some 75% of the galaxies are elliptical. This clustering also suggests that they formed a long time ago, because galaxies are likely to have formed first in high-density regions like galaxy clusters.

The largest galaxies in the universe are giant elliptical galaxies. They can contain a trillion stars or more, and span as much as two million light-years - about 20 times the width of the Milky Way. Some of them appear to contain supermassive black holes at their hearts - star-gobbling monsters that are as much as three billion times as heavy as the Sun. These giant ellipticals are often found in the hearts of galaxy clusters.

### Spirals

Spiral galaxies like the one to the left have flat disks of stars with bright bulges called nuclei in their centers. Spiral arms wrap around these bulges. An extended spherical halo of stars envelops the nuclei and arms. Spiral arms probably form as the result of waves that sweep through the galactic disk. Like the waves on the ocean, these so-called "density waves" don't carry any material with them - they move by disrupting the material they pass through. In the case of galaxies, density waves squeeze clouds of interstellar gas, causing new stars to form inside the clouds. Some newborn stars are massive, hot, and bright, so they make the spiral arms appear bright. These massive stars are blue or white, so the spiral arms look blue-white, too. When viewed edge-on, the spiral arms often appear as dark lanes, because they contain lots of interstellar dust that blocks the light from the bulge. The gaps between the arms contain older stars, which are not as bright. However, the bulges of spirals are often red, like elliptical galaxies, suggesting that they are composed of older stars.

In some spirals, the density wave organizes the stars in the center into a bar. The arms of barred spiral galaxies spiral outward from the ends of the bar. The Milky Way may fall into this class of spirals, called barred spirals.

In the Hubble tuning fork system, normal spirals are designated "S" and the barred varieties "SB." Each of these classes is subclassified into three types according to the size of the nucleus and the degree to which the spiral arms are coiled. The three subclasses are denoted with the lowercase letters "a," "b," and "c." Some galaxies are also intermediate between ellipticals and spirals. These intermediate galaxies have the disk shape characteristic of spirals, but have no spiral arms. These intermediate forms bear the designation "S0." Three spiral galaxies are shown below.

### Irregulars

The final class of galaxies, "irregulars," contains a hodge-podge of shapes - anything that looks neither spiral nor elliptical. Any galaxy with no identifiable form - whose stars, gas, and dust are spread randomly - is classified as irregular. Irregulars are the smallest galaxies, and they may contain as few as one million stars. They may be the "building blocks" that came together to form the first large galaxies. Many small irregular galaxies orbit the Milky Way, including the Large and Small Magellanic Clouds.

Hubble recognized two types of irregular galaxies, Irr I and Irr II. Irr I is the most common type of irregular galaxy. This type and seems to be an extension of the spiral classes, beyond Sc, into galaxies with no discernible spiral structure. Irr I galaxies are blue, highly resolved, and have little or no nucleus. Irr II galaxies are rare. This type includes various kinds of chaotic galaxies, which appear to have formed in many different ways.

### Quasars

Quasars were first discovered in the early 1960s when radio astronomers identified a small star designated 3C 48 that emitted powerful radio waves. When they measured the spectrum of the star, they found something completely unexpected: the spectrum was flat with several unexpected, and totally unexplainable, emission lines. The object remained a mystery until similar but brighter object, 3C 273, was discovered in 1963. Astronomers noticed that 3C 273 had a normal spectrum with the same emission lines as observed in radio galaxies, but the spectrum had been greatly redshifted (that is, spectral lines were found at longer wavelengths than expected). This observation explained the mystery of 3C 48's spectrum: it was an ordinary spectrum from a radio galaxy, but it was so redshifted that familiar spectral lines were so far from where they should have been that no one recognized them. When an object moves away from us, its spectral lines are redshifted; the faster it moves, the greater the redshift. If 3C 273's redshift were to be due to its velocity, however, its velocity would have to be faster than the speed of light - which is impossible. Many more such objects were found, and they came to be known as quasi-stellar radio sources, abbreviated as quasars.

Today, we know that quasars are galaxies with extremely energetic nuclei. The amount of radiation emitted by such a nucleus overwhelms the light from the rest of the galaxy, so that only special observational techniques can reveal the rest of the galaxy's existence. The nucleus explains why quasars appear starlike - all we can see is the bright central engine.

Although the nucleus of a quasar is extremely small - only the size of the Solar System - it emits up to 100 times as much radiation as an entire galaxy. The galaxy underlying the brilliant image of a quasar is probably fairly normal, except for the superficial large-scale effects of the quasar at its center. Quasars are thought to be powered by supermassive black holes at the centers of galaxies. The powerful radiation we see comes from matter swirling around and falling into the black hole.

The SDSS (and sky surveys that use visible light) can find distant quasars at redshifts of 4-6, or 90% as old as the universe itself, because quasars look like stars but have peculiar colors. By searching for faint starlike objects and taking their spectra, the SDSS is expected to find thousands of quasars at redshifts greater than 4. The most distant quasar yet discovered, at a redshift of 6.4, was seen by the SDSS in January 2003.

### How lightning rod works?

The lightning rod, which Benjamin Franklin invented in 1749, is a metal pole mounted atop a building that draws lightning's electrical charge away from the structure.The rod is attached to an aluminium or copper cable that's connected to an underground conductive grid. This allows the electricity to dissipate harmlessly.
Because lightning tends to strike the tallest object in the vicinity, lightning rods must be taller than any buildings or other objects in the area.If installed properly, a lightning rod will carry a lightning bolt's electrical charge through the path of least resistance along the cable into the ground, reducing the risk of fire or heat damage from the strike.

Lightning looks for the easiest path to travel and lightning rods are good conductors of electrical current. If lightning strikes the rod, the electrical current is moved away from the house and is safely gotten rid of underground. Sometimes lightning strikes and then jumps around a bit, looking for a better path. If a lightning rod is nearby, the lightning can move over to it. This avoids more damage after the lightning has already struck.

### GEIGER COUNTER

INTRODUCTION
Geiger counter is a portable device which is used for the detection and counting of ionized particles and radiation

CONSTRUCTION
It consists of a hollow metallic cylinder, one end of which is closed by an insulating cap. At the center of the cap is fixed a stiff straight wire along the axis of cylinder .A thin mica or glass disc closes the other end which also serves as the entrance window for ionizing particles. The tube contains a special mixture of air, argon, alcohol at a pressure of 50-100 mmHg.

WORKING

A potential difference of the range of 1000V is maintained between the metal cylinder and the axial wire through a suitable series resistor of 109 ohms. When an ionizing particle enters the tube through the window, it ionizes some gas molecules in it. These ions are accelerated by the strong radial electric field producing more ions by collision which produces ionization current so a momentary current flows between the wire and the cylinder and also through the resistor R. The ends of “R” are connected to a loud speaker or an electronic counter.

COUNTING OF PARTICLES
Each time a  particle enters the counter and ionization current pulse is created which gives a click in the loud speaker or a count in a counter.
In the case of ionizing radiation, the numbers of counts register by the counter measures the intensity or ionizing power of incident radiation.

### WILSON CLOUD CHAMBER

INTRODUCTION
It is an instrument used for the detection and identification of the path of subatomic particles.
In Wilson Cloud Chamber, paths of subatomic particles or ionized particles can be photographed.

WORKING PRINCIPLE

When a particle is passed through the supersaturated vapours, droplets are formed on the line due
to ionization along the track and particle is detected.

CONSTRUCTION
It is consist of a closed cylinderical chamber with the transparent glass top,a movable piston at the bottom. On the sides near the top, the cylinder is provided with a glass window. inside the cylinder
a liquid of low boiling point is placed. The piston can be moved up or down. The whole system is air tight.A strong light source isused to illuminate the chamber while the photograph is taken by the
camera as shown.

WORKING

Some volatile liquid having low boiling point (methanol CH3OH or ethanol C2H5OH) is poured on the inner surface of the chamber. The piston first is moved slowly up so that the air inside the chamber is cleaned and then it is then moved down, so that the internal pressure is dropped and the air get vapours of the liquid and becomes supersaturated and a fog is observed in the chamber.

At the right moment particles are allowed to enter into the chamber and a powerful and intense beam of light is used to illuminate the track of the particles

and photos are taken by the sensitive camera.
If a strong electric or magnetic field is applied to the particles (charged) then their path is altered.
By the study of path`s length, thickness, continuity or discontuinity and the influence of magnetic
field (curve) .i.e. geometry the e/m ratio can be calculated and hence the particle is detected.

### Working of SCR - Silicon Controlled Rectifiers

In solid state S/C silicon controlled rectifier , anode terminal is always kept at positive potential w.r.t cathode terminal. The load is connected in the series with the anode .

The working of SCR circuit can be grouped as followings:

When gate is open:In the SCR circuit with no voltage is applied to the gate i.e open gate,junction J2 is reverse biased whereas J1 and J3 is forward biased connection . Therefore , the condition in the junction J1 and J3 is as similar as npn transistor with base open .As a result no current flows via the load resister RL.,at that time the SCR is cut off state.If the applied voltage in the circuit is slightly increased ,a stage is reached when junction J2 breakdown because of reverse biased . Now the SCR conducts rapidely and at that time SCR side to be ON state .The amount of the applied voltage at which SCR conducts rapidely with open gate is called break over voltage.

When gate voltage is applied : When the gate terminal is positive w.r.t cathode , here junction J1 and J3 is forward biased where as the junction J2 is reverse biased.When small gate voltage is applied the SCR conduct heavily. In proper biasing condition ,the electron starts to move from n-type material to cross junction J3 towards left and holes from p-type material towards right .As a result ,electrons attracted across the junction J2 and gate current flows ,the anode current heavily increase .Consequently more electron available at junction J2 .This process run continues ,So junction J2 breaks down at an extremely small time and the SCR starts conducts heavily in the circuit .Once the SCR starts to conducts ,the gate loses its control properties .If gate voltage is removed ,even the anode current conducts heavily in the circuit. To stop current conduction , the applied voltage is reduced to zero voltage.

Conclusion:The following conclusions are drawn out from the working principles of SCR:

1.An SCR has two state ,one is ON state and other is OF state(i.e either is conducts heavily or does not conducts ). So SCR behaves like electronics switch.
2.On the SCR ,there are two ways to run the SCR as electronics switch.The first ways is to keep the gate open and make applied voltage equal to the break over voltage .The second ways is to apply the gate voltage ,and supply voltage is less than break over voltage.
3.When the gate voltage is applied then the break over voltage is always much greater than supply voltage .
To makes SCR non-conducting (ie open the SCR),reduce the supply voltage to zero.

### What is Boyle's Law?

Boyle studied the compressibility of gases in 1660. In his experiments he observed "At a fixed temperature, the volume of a gas is inversely proportional to the pressure exerted by the gas." The experiment is simple: (see figure on right)

A cylinder with a piston and a gas is immersed in a bath (e.g. water). The purpose of the bath is to have a ready heat source to maintain the temperature of the gas constant throughout the experiment. A mass is placed on top of the piston which results in a pressure on the gas. The gas volume is measured and 1/V vs P data point plotted. The mass is increased and the new 1/V vs P data point plotted. This is continued over several larger masses. to see what happens place the mouse cursor over the image.

The straight line impliesor

Which is Boyle's law.

### Why pair production can not take place in vacuum?

The most basic conservation laws are conservation of energy, conservation of momentum and conservation of angular momentum. These laws are a result of the invariance of the fundamental equations of motion to moving the origin or rotating the axes of our coordinate system. In other words, the fundamental equations should look the same, regardless of how we choose our coordinate system. The mathematical theorem which relates the existence of these conservation laws to the invariance of the equations is called Noether's Theorem.

The reason why a gamma-ray cannot create electron-positron pairs in a vacuum is that there is no way to do this without violating the conservation laws. Another fundamental invariance of the equations is Lorentz invariance, which means that the fundamental equations should look the same in all coordinate systems which can be related by a Lorentz transformation. A Lorentz transformation relates the equations in one coordinate system with the equations in another coordinate system which is moving with a constant velocity with respect to the first one. Under a Lorentz transformation the gamma-ray undergoes a Doppler shift. That means its energy and momentum are changed. We can choose a Lorentz transformation under which the energy of the gamma-ray becomes too small to create an electron-positron pair.

The physical process must be the same, regardless of which coordinate system we choose to describe it in. Therefore, it must be impossible for the isolated gamma-ray to create a pair in any coordinate system. Obviously, the argument is the same for the creation of proton-antiproton pairs, etc. If we started with two gamma-rays moving in opposite directions, then the gamma-rays could collide with each other, and create a particle- antiparticle pair. In this case, when we try to make a Lorentz transformation which Doppler-shifts the energy of one gamma-ray to low energy, the energy of the other gamma-ray will be Doppler-shifted to a higher energy. The sum of the energies of the two gamma-rays is the smallest in the coordinate system in which their total momentum is zero. Thus, if they can create an electron-positron pair in this coordinate system, they can do it in any Lorentz-transformed coordinate system.

There must always be another particle present which can be manipulated so the total momentum of all particles is conserved before & after pair production.

### What happens to capacitance of parallel plate capacitor when the size of plates increase and distance between them decrease?

There are three basic factors of capacitor construction determining the amount of capacitance created. These factors all dictate capacitance by affecting how much electric field flux (relative difference of electrons between plates) will develop for a given amount of electric field force (voltage between the two plates):

PLATE AREA: All other factors being equal, greater plate area gives greater capacitance; less plate area gives less capacitance.

Explanation: Larger plate area results in more field flux (charge collected on the plates) for a given field force (voltage across the plates).

PLATE SPACING: All other factors being equal, further plate spacing gives less capacitance; closer plate spacing gives greater capacitance.

Explanation: Closer spacing results in a greater field force (voltage across the capacitor divided by the distance between the plates), which results in a greater field flux (charge collected on the plates) for any given voltage applied across the plates.

DIELECTRIC MATERIAL: All other factors being equal, greater permittivity of the dielectric gives greater capacitance; less permittivity of the dielectric gives less capacitance.

Explanation: Although its complicated to explain, some materials offer less opposition to field flux for a given amount of field force. Materials with a greater permittivity allow for more field flux (offer less opposition), and thus a greater collected charge, for any given amount of field force (applied voltage).

"Relative" permittivity means the permittivity of a material, relative to that of a pure vacuum. The greater the number, the greater the permittivity of the material. Glass, for instance, with a relative permittivity of 7, has seven times the permittivity of a pure vacuum, and consequently will allow for the establishment of an electric field flux seven times stronger than that of a vacuum, all other factors being equal.

### How do electrons and holes flow in a transistor ?

We will now explain the operation for the transistor, using an NPN type. The same operation applies for the PNP transistors as well, but with currents and voltage sources reversed.

With no power applied to the transistor areas,
there are two depletion zones between the two P-N contacts. Suppose now that we connect a power source between the base and the collector in reverse-bias, with the positive of the source connected to the collector and the negative to the base. The depletion zone of the P-N contact between the base and the collector will be widened. Moreover, a slight current will flow withing this contact (due to impurities). This current is the reverse contact current and we will use the symbol ICBO:

Now suppose that we connect another voltage supply between the emitter and the base in forward bias, with the positive of the source connected to the base and the negative connected to the emitter. The depletion zone between the emitter and the base will be shortened, and current (electrons) will flow when the voltage exceeds a specific level. This level depends on the material that the transistor is made of. Germanium (Ge) is the material that was originally used to make transistor, and later Silicon (Si) was used. For Germanium, the voltage is around 0.3 volts (0.27 @ 25oC), and for Silicon the voltage is around 0.7 volts (0.71 @ 25oC). Some of the electrons that go through the e-b depletion zone, will re-connect with holes in the base. This is the base current and we will use the IB symbol for reference. In real life, this current is at the scale of micro-amperes (Î¼A or uA):

But most of the electrons will flow through the base (due to spilling) and will be directed to the collector. When these electrons reach the depletion area between the base and the collector, they will experience a force from the electric field which exists in this zone, and the electrons will pass through the depletion zone. The electrons will then re-connect with holes in the collector. The re-connected holes will be replaced with holes coming from the base-collector power supply (VCC). The movement of these holes equals to a movement of electrons in the opposite direction, from the collector to the supply. In other words, the current that flows to the emitter will be divided into the small base current and the larger collector current:

IE = IB + IC

Generally, the number of electrons that arrive at the collector is the 99% of the total electrons, and the rest 1% causes the base current.

At the collector, except the electrons that come from the emitter, there is also the reverse current from the base-collector contact that we saw before. Both currents flow at the same direction, so they are added:

IC' = IC + ICBO

The following drawing shows how the electrons and holes flow within the transistor:

This is generally what happens inside a transistor when voltage is applied. The purpose of this theory is to explain how can someone use the transistor to design an amplifier or a switch, so we will not go into many details. It is enough to know this basic operation.