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Free Kick and Physics

One footballing situation particularly stands out as relevant to physicists: the free kick.

Since the goal is typically defended with a wall of players, scoring a goal means that the attacking player must bend the ball around that wall. Doing so takes advantage of a phenomenon known as the Magnus Effect, after Gustav Magnus who investigated it in 1852.

Striking the ball off-centre gives it a spin, which changes the airflow around the ball and creates a turbulent wake. The airflow is deflected in the direction of spin, giving the ball a horizontal force and resultant motion.

The amount of curvature in the ball’s path can also increase mid-flight. This happens when the ball slows enough that the airflow around it instantaneously changes from chaotic flow  to laminar flow. The air pressure on the ball, and therefore the drag it experiences, increases, slowing it down further and heightening the influence of the Magnus Effect. (In the absence of gravity, the ball would eventually produce a spiral flightpath.)

It’s a tough skill to get right – only about a tenth of direct free kicks in the English top flight find the back of the net. The structure of the ball and atmospheric disturbances within the stadium can have an effect.

But ultimately the amount of curvature produced mainly depends on the coefficient of friction between ball and boot, how far off-centre it’s struck, and its speed. So to bend it like Beckham, kick a dry ball at an angle – and belt it hard.

Weird Rainbows

Upside down rainbows

Upside down rainbows, or ‘circumzenithal arcs’, to give them the proper name, are not caused by rain. Normal rainbows form when light refracts through raindrops, mist, or sometimes even sea spray. The upside down kind however, are caused by ice crystals in the air. They are more common in cold climates, but still fairly rare.

Double rainbows

Double rainbows occur when the sunlight is reflected twice inside the raindrops. The second rainbow usually sits outside the first, and looks dimmer and more blurry than the original. Because of the angle of reflection, the second rainbow appears with the opposite colour scheme to the first.

Supernumerary rainbows

It sounds complicated, but really a supernumerary rainbow is one with smaller repeating rainbows inside it. The smaller rainbows tend not to have the same colour patterns as a normal rainbow, and the colours are lighter.

How does an ice pyramid work?

Ice Spikes
If you go out one morning, just as the temperature has really started to drop, you might be forgiven for thinking that tiny aliens landed in your birdbath during the night. Birdbaths, as still pools of water that are left out in freezing conditions, are the most likely place to see inverted ice pyramids.

 Regular ice spikes form because, at just the right temperature, the sides and top of a body of water - usually water in an ice cube tray - freeze first. As they freeze they expand, putting pressure on the water in the middle. If there is a tiny hole in the ice forming at the surface of the still-hardening cube, the liquid water is pushed upwards. The water pushed up through the hole forms a little frozen mound on the top of the ice cube. This little mound also has a hole in its center, through which more water is pushed, and the whole thing builds up into a spike.

Ice pyramids form through a variation on the process.The water doesn't freeze continuously, moving from the sides of the container to the middle. It freezes in what can best be described as "sheets." These sheets hang down vertically from the surface of the water. Sometimes they can be parallel to each other, as if someone were taking orderly slices from the water. Other times they can form at all angles to each other.

Inverted pyramids are formed when these sheets are at just the right angle to each other. Essentially, they form the shape, or the mold, for the pyramid under the water. In the meantime, the surface of the water freezes in roughly the shape of the pyramid base. At that point, the only way for the pyramid to go is up and out of the water. The only important part is that the "tip" of the pyramid doesn't freeze over, so more water can be forced into the pyramid "mold." As they ice sheets keep freezing and expanding, the pyramid is pushed up and up. Because the sheets are freezing, the underwater mold is getting smaller, the pyramid eventually tapers off to a point.

Eventually, the entire thing is frozen in place, waiting for people to be astonished by it the next morning. If you have a pond, a bird bath, or any small body of water that can freeze over, keep an eye out for an ice spike. Under the right conditions, the "spikes" can be pyramids, "cubes," or even vases.

What is a gravitational wave?

What is a gravitational wave?

A gravitational wave* is a concept predicted by Einstein's theory of general relativity. General relativity states that mass distorts both space and time in the same way a heavy bowling ball will distort a trampoline.

When an object accelerates, it creates ripples in space-time, just like a boat causes ripples in a pond (and also similarly an accelerating electrical charge produces an electromagnetic wave). These space-time ripples are gravitational waves. They are extremely weak so are very difficult to detect. Missions like LISA or LIGO hope to spot gravitation waves detecting small changes in the distances between objects at set distances; satellites for LISA and mirrors for LIGO. As the strength of the wave depends on the mass of the object our best hope of detecting gravitational waves comes from detecting two black holes or pulsars collapsing into each other.

Gravitational waves have been inferred from watching two pulsars spinning and noticing they are slowing down, due to losing energy from emitting gravitational waves.

Gravitational waves are important in telling us about the early universe. The cosmic microwave background gives us a snapshot of the universe about 380,000 years after the start of the universe. Looking very closely at the cosmic microwave background there are patterns seen which can are also be measured in the large scale structure of the universe (so galaxies and clusters) today. These patterns in the cosmic microwave background were caused by very tiny random perturbations from the time when the universe expanded rapidly, known as inflation.

Inflation should also generate gravitational waves. These waves affect the polarization (the way the wave oscillates) of the cosmic microwave background. Measuring the strength of the polarization due to gravitational waves gives us a ballpark figure of the amount of energy involved at the time of inflation and helps pin down when inflation occurred.

*Not to be confused with a gravity wave (which is a wave driven by the force of gravity).

How do speakers work?

Q.How do speakers work?

A. Speakers come in all shapes and sizes, enabling you to listen to music on your iPod, enjoy a film at the cinema or hear a friend’s voice over the phone.

In order to translate an electrical signal into an audible sound, speakers contain an electromagnet: a metal coil which creates a magnetic field when an electric current flows through it. This coil behaves much like a normal (permanent) magnet, with one particularly handy property: reversing the direction of the current in the coil flips the poles of the magnet.

Inside a speaker, an electromagnet is placed in front of a permanent magnet. The permanent magnet is fixed firmly into position whereas the electromagnet is mobile. As pulses of electricity pass through the coil of the electromagnet, the direction of its magnetic field is rapidly changed. This means that it is in turn attracted to and repelled from the permanent magnet, vibrating back and forth.

The electromagnet is attached to a cone made of a flexible material such as paper or plastic which amplifies these vibrations, pumping sound waves into the surrounding air and towards your ears.

Inside a speaker:
1. Cone
2. Electromagnet (coil)
3. Permanent magnet

The frequency of the vibrations governs the pitch of the sound produced, and their amplitude affects the volume – turn your stereo up high enough and you might even be able to see the diaphragm covering the cone move.

To reproduce all the different frequencies of sound in a piece of music faithfully, top quality speakers typically use different sized cones dedicated to high, medium and low frequencies.

A microphone uses the same mechanism as a speaker in reverse to convert sound into an electrical signal. In fact, you can even use a pair of headphones as a microphone!

How does GPS(Global Positioning System) work?

Q. How does GPS(Global Positioning System) work?

A. The Global Positioning System (GPS) is a network of about 30 satellites orbiting the Earth at an altitude of 20,000 km. The system was originally developed by the US government for military navigation but now anyone with a GPS device, be it a SatNav, mobile phone or handheld GPS unit, can receive the radio signals that the satellites broadcast.

Wherever you are on the planet, at least four GPS satellites are ‘visible’ at any time. Each one transmits information about its position and the current time at regular intervals. These signals, travelling at the speed of light, are intercepted by your GPS receiver, which calculates how far away each satellite is based on how long it took for the messages to arrive.

Once it has information on how far away at least three satellites are, your GPS receiver can pinpoint your location using a process called trilateration.


Imagine you are standing somewhere on Earth with three satellites in the sky above you. If you know how far away you are from satellite A, then you know you must be located somewhere on the red circle. If you do the same for satellites B and C, you can work out your location by seeing where the three circles intersect. This is just what your GPS receiver does, although it uses overlapping spheres rather than circles.

The more satellites there are above the horizon the more accurately your GPS unit can determine where you are.

GPS and Relativity

GPS satellites have atomic clocks on board to keep accurate time. General and Special Relativity however predict that differences will appear between these clocks and an identical clock on Earth.

General Relativity predicts that time will appear to run slower under stronger gravitational pull – the clocks on board the satellites will therefore seem to run faster than a clock on Earth.

Furthermore, Special Relativity predicts that because the satellites’ clocks are moving relative to a clock on Earth, they will appear to run slower.

The whole GPS network has to make allowances for these effects –  proof that Relativity has a real impact.

Why Do We Always See the Same Side of the Moon?

Q: Why does the moon always present the same face to us? I find it impossible to believe that this could happen by chance.

A: Nope, not by chance — it’s pure physics.

For starters, the moon is not stuck in place with one side facing us. Our lunar companion rotates while it orbits Earth. It’s just that the amount of time it takes the moon to complete a revolution on its axis is the same it takes to circle our planet — about 27 days. As a result, the same lunar hemisphere always faces Earth.

How’d this come to be? In a word: gravity. The moon’s gravity slightly warps our planet’s shape and gives us tides. Likewise, Earth tugs at the moon, creating a rocky, high-tide “bulge” facing us. That bulge ended up working like a brake, slowing the moon’s spin down to the current rate, so the lunar high tide permanently faces us.

When that happened, about 4 billion years ago, the moon became “tidally locked,” and it has presented us the same visage ever since.

MIT Course 8.02 :Electricity and Magnetism( Study Material)

Course Highlights

This course features a complete set of videotaped lectures. The 36 video lectures on Electricity and Magnetism, by Professor Lewin, were recorded on the MIT campus during the Spring of 2002. Prof. Lewin is well-known at MIT and beyond for his dynamic and engaging lecture style.

Course Description
In addition to the basic concepts of Electromagnetism, a vast variety of interesting topics are covered in this course: Lightning, Pacemakers, Electric Shock Treatment, Electrocardiograms, Metal Detectors, Musical Instruments, Magnetic Levitation, Bullet Trains, Electric Motors, Radios, TV, Car Coils, Superconductivity, Aurora Borealis, Rainbows, Radio Telescopes, Interferometers, Particle Accelerators (a.k.a. Atom Smashers or Colliders), Mass Spectrometers, Red Sunsets, Blue Skies, Haloes around Sun and Moon, Color Perception, Doppler Effect, Big-Bang Cosmology.

What is Elastic Potential Energy?

Elastic Potential Energy

Any object than can be deformed (have its shaped changed) and then return to its original shape can store elastic potential energy.
• We’re still talking about potential energy, since it is stored energy until the object is allowed to
bounce back.
• “Elastic” does not refer to just things like elastic bands…other materials that would be referred
to as elastic would be
• pole vaulter’s pole
• springs

You learned in Physics that Hooke’s Law is…
F = kx
F = force (N)
k = spring constant for that object (N/m)
x = amount of expansion or compression (m)
We can use this formula to figure out a formula for the energy stored in the spring.
• Remember that W = F d

• We might be tempted to just shove the formula for Hooke’s Law into this formula to get
W = kxd = kx2
, but this is wrong!
• You have to take into account that the force is not constant as the object returns to its original
shape… it’s at a maximum when it is deformed the most, and is zero when the object is not
• Let’s graph Force vs Distance of Expansion for a spring that was stretched and we are now
letting go of it…

But this is really just a Force vs Displacement Graph like the ones we just looked at a couple of
sections back! To figure out the energy of the spring we can just figure out the work it does by looking at the area under the graph.

Area = ½ bh
 = ½ F x
 = ½ (kx) x
Area = ½ kx2 = W
So the work done by the spring (and then energy it stored) can be calculated using…
Ee = ½ kx2
Ee = eleastic potential energy (J)
k = spring constant (N/m)
x = amount of expansion or compression [deformation] (m)

Example 1: Determine how much energy a spring with a spring constant of 15 N/m stores if it is
stretched by 1.6m.
Ee = ½ kx2
 = ½ (15N/m) (1.6 m)
Ee = 19 J

If scientists can't see dark matter, how do they know it exists?

Q.If scientists can't see dark matter, how do they know it exists?

Ans. Scientists calculate the mass of large objects in space by studying their motion. Astronomers examining spiral galaxies in the 1950s expected to see material in the center moving faster than on the outer edges. Instead, they found the stars in both locations traveled at the same velocity, indicating the galaxies contained more mass than could be seen. Studies of the gas within elliptical galaxies also indicated a need for more mass than found in visible objects. Clusters of galaxies would fly apart if the only mass they contained were visible to conventional astronomical measurements.

Albert Einstein showed that massive objects in the universe bend and distort light, allowing them to be used as lenses. By studying how light is distorted by galaxy clusters, astronomers have been able to create a map of dark matter in the universe.

Although dark matter makes up most of the matter of the universe, it only makes up about a quarter of the composition. The universe is dominated by dark energy.

After the Big Bang, the universe began expanding outward. Scientists once thought that it would eventually run out of the energy, slowing down as gravity pulled the objects inside it together. But studies of distant supernovae revealed that the universe today is expanding faster than it was in the past, not slower, indicating that the expansion is accelerating. This would only be possible if the universe contained enough energy to overcome gravity — dark energy.

All of these methods provide a strong indication that the most of the matter in the universe is something yet unseen.

What is the Physics Behind Vacuum Cleaner?

When you sip soda through a straw, you are utilizing the simplest of all suction mechanisms. Sucking the soda up causes a pressure drop between the bottom of the straw and the top of the straw. With greater fluid pressure at the bottom than the top, the soda is pushed up to your mouth. ­
This is the same basic mechanism at work in a vacuum cleaner, though the execution is a bit more complicated. In this article, we'll look inside a vacuum cleaner to find out how it puts suction to work when cleaning up the dust and debris in your house. As we'll see, the standard vacuum cleaner design is exceedingly simple, but it relies on a host of physical principles to clean effectively.

It may look like a complicated machine, but the conventional vacuum cleaner is actually made up of only six essential components:

An intake port, which may include a variety of cleaning accessories
An exhaust port
An electric motor
A fan
A porous bag
A housing that contains all the other components

When you plug the vacuum cleaner in and turn it on, this is what happens:
The electric current operates the motor. The motor is attached to the fan, which has angled blades (like an airplane propeller).
As the fan blades turn, they force air forward, toward the exhaust port (check out How Airplanes Work to find out what causes this).
When air particles are driven forward, the density of particles (and therefore the air pressure) increases in front of the fan and decreases behind the fan.
This pressure drop behind the fan is just like the pressure drop in the straw when you sip from your drink. The pressure level in the area behind the fan drops below the pressure level outside the vacuum cleaner (the ambient air pressure). This creates suction, a partial vacuum, inside the vacuum cleaner. The ambient air pushes itself into the vacuum cleaner through the intake port because the air pressure inside the vacuum cleaner is lower than the pressure outside.
As long as the fan is running and the passageway through the vacuum cleaner remains open, there is a constant stream of air moving through the intake port and out the exhaust port. But how does a flowing stream of air collect the dirt and debris from your carpet? The key principle is friction.

Kaniz e zehra asked What is Heat?

11/13/2014 10:06:13 Kaniz e zehra asked What is Heat?

Consider a very hot mug of coffee on the countertop of your kitchen. For discussion purposes, we will say that the cup of coffee has a temperature of 80°C and that the surroundings (countertop, air in the kitchen, etc.) has a temperature of 26°C. What do you suppose will happen in this situation? I suspect that you know that the cup of coffee will gradually cool down over time. At 80°C, you wouldn't dare drink the coffee. Even the coffee mug will likely be too hot to touch. But over time, both the coffee mug and the coffee will cool down. Soon it will be at a drinkable temperature. And if you resist the temptation to drink the coffee, it will eventually reach room temperature. The coffee cools from 80°C to about 26°C. So what is happening over the course of time to cause the coffee to cool down? The answer to this question can be both macroscopic and particulate in nature.

On the macroscopic level, we would say that the coffee and the mug are transferring heat to the surroundings. This transfer of heat occurs from the hot coffee and hot mug to the surrounding air. The fact that the coffee lowers its temperature is a sign that the average kinetic energy of its particles is decreasing. The coffee is losing energy. The mug is also lowering its temperature; the average kinetic energy of its particles is also decreasing. The mug is also losing energy. The energy that is lost by the coffee and the mug is being transferred to the colder surroundings. We refer to this transfer of energy from the coffee and the mug to the surrounding air and countertop as heat. In this sense, heat is simply the transfer of energy from a hot object to a colder object.

Now let's consider a different scenario - that of a cold can of pop placed on the same kitchen counter. For discussion purposes, we will say that the pop and the can which contains it has a temperature of 5°C and that the surroundings (countertop, air in the kitchen, etc.) has a temperature of 26°C. What will happen to the cold can of pop over the course of time? Once more, I suspect that you know the answer. The cold pop and the container will both warm up to room temperature. But what is happening to cause these colder-than-room-temperature objects to increase their temperature? Is the cold escaping from the pop and its container? No! There is no such thing as the cold escaping or leaking. Rather, our explanation is very similar to the explanation used to explain why the coffee cools down. There is a heat transfer.

Over time, the pop and the container increase their temperature. The temperature rises from 5°C to nearly 26°C. This increase in temperature is a sign that the average kinetic energy of the particles within the pop and the container is increasing. In order for the particles within the pop and the container to increase their kinetic energy, they must be gaining energy from somewhere. But from where? Energy is being transferred from the surroundings (countertop, air in the kitchen, etc.) in the form of heat. Just as in the case of the cooling coffee mug, energy is being transferred from the higher temperature objects to the lower temperature object. Once more, this is known as heat - the transfer of energy from the higher temperature object to a lower temperature object.

Kaniz e zehra asked Two unlike capacitor is charged to a certain potential difference it is then immersed in oil what happen to it s capacitance ,charge and potential?

11/13/2014 9:49:27 Kaniz e zehra asked Two unlike capacitor is charged to a certain potential difference it is then immersed in oil what happen to it s capacitance ,charge and potential?

Ans.If you mean that an air capacitor is charged to a certain potential difference it is then immersed in oil what happen to it’s a)charge b)Potential and c) capacitance
Then the answer is :The dielectric constant Єr of the oil is grater than that of air.Whan an air capacitor is immersed in oil then
a)Its charge remain constant b)PD b/w the plates decreases c)the Capacitance increase.

But if the questions inlove two capacitors then the question will be same what like :Two unlike capacitors of different potentials and charges are joined in parallel.what happens to their pD?How are their charges distributed ?Is the energy of system affected? then answer will be :i)The potential difference will remain same.(ii) The charge is distributed (iii)The energy of the system decrease

What is Voltage?

Voltage is electric potential energy per unit charge, measured in joules per coulomb ( = volts). It is often referred to as "electric potential", which then must be distinguished from electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. Like mechanical potential energy, the zero of potential can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful. The difference in voltage measured when moving from point A to point B is equal to the work which would have to be done, per unit charge, against the electric field to move the charge from A to B.

What is the Physics Behind Walking on Broken Glass?

For this demonstration the glass bottles should first be soaked in water to remove any paper labels. An alternative is to use Mason jars. It is best to use fairly large bottles so that the pieces formed will have only a gentle curve to them. When breaking the bottles I place them in a canvas sack and use a hammer, being sure to wear gloves and eye protection. The glass should be broken into fairly small pieces. The bed for the glass may be made from half-inch-thick plywood framed by pieces of 2"34” wood. Once the glass has been poured into the bed it should be spread out to a uniform depth. Any piece that has a right-angled bend in it, where the sidewall of the bottle meets the base, is moved to the edges of the bed so that only relatively flat pieces of glass are included in the center of the bed where the walking takes place. As an extra precaution, I cover the glass with a cloth and then use a large cast iron skillet to pound the surface firmly. This ensures no points of glass are sticking up. This is usually done before the audience enters the room. A bed of glass about 8 cm (three inches) deep seems best, as this provides sufficient depth for the glass to be able to shift and settle somewhat as a foot is planted slowly and directly down upon it. When done this way the pieces of glass lay fairly flat and no edge presses perpendicularly against the sole. The bottom of the foot has some give to it and conforms to the shallow curve of the glass pieces. This is similar to a sharp knife being pressed with the flat of the blade against one’s flesh, where considerable force may be used without injury. When walking I place each foot slowly, moving it elsewhere if a point or edge is felt, although that is seldom necessary if the bed has been prepared correctly. Care must be taken to brush off any pieces of glass that stick to the bottom of the feet when stepping off the bed.

To show that the edges of the glass are sharp I use a piece from the bed to cut the string suspending a bowling ball about a half meter (two feet) above the floor.

What is proof of Kepler law of planetary motion that all planet has elliptical orbit? And why they have elliptical orbit instead of a circular orbit?

The orbit of a planet is an ellipse where one focus of the ellipse is the sun.

An ellipse is defined by two focii and all points for which the sum of the distances are the same. The semimajor axis (a) is the long distance from the center to edge of the ellipse. If r1 and r2 are the distances from the focii to any point on the ellipse then r1 + r2 = 2a. The short axis is called the semiminor axis.

How “elliptical” an orbit is can be described by the eccentricity(e). The eccentricity is equal to the distance between a focus and the center (c) of the ellipses divided by the semimajor axis (a). That is, e = c/a. 

See the elementary proof: View

What multiple of distance between the centre of the earth and that of the moon is the distance between the centre of the earth and the geostationary satelite which always stays above the fixed location on the equator ? take the cycle of revolution of the moomn around the earth to be 27 days ?

According to Kepler’s third law of planetary motion
T2=R3 ( For geo stationary satellite)-------1
T’2=R’3( For Moon)----------------------------2
Dividing eq(2) by eq(1), we get
T’2 / T2=R’3/ R3
Since T’=27 T
Then we can write as
27 T2 /T2= R’3/ R3
R’3=27 R3

R’=3 R
R= 1/3 R'
so the distance between the centre of the earth and the geostationary satellite which always stays above the fixed location on the equator is 1/3 times distance between the centre of the earth and that of the moon .

Where can I see the aurora?

Auroras usually occur in ring-shaped areas centered around the magnetic poles of Earth. The complete rings, called the auroral ovals, can only be seen from space. False color picture of the auroral oval in ultraviolet light. The brighter the color, the more intense the aurora.  The crescent of color on the left is from sunlight
scattered over the upper atmosphere. The best places to see the aurora are in Alaska, Canada, and Scandinavia, during the late evening hours.  Resident of the northernmost United States – near the Canadian border – typically see auroras several times a year.  On rare occasions – perhaps once per decade – auroras are visible as far south as Florida or Japan.

Why does aurora take different shapes?

Scientists are still trying to answer this question.  The shape of the aurora depends on where in the magnetosphere the electrons came from and on what caused them to precipitate into the atmosphere. Dramatically different auroral shapes can be seen in a single night.

Why the different colors formed in aurora?

The color of the aurora depends on which gas is being excited by the electrons and on how much energy is being exchanged. Oxygen emits either a greenish-yellow light  (the most familiar color of the aurora) or a red light; nitrogen generally gives off a blue light.  The oxygen and nitrogen molecules also emit ultraviolet light, which can only be detected by
special cameras on satellites

What causes the aurora?

The “northern lights” are caused by collisions between fast-moving particles (electrons) from space and the oxygen and nitrogen gas in our atmosphere.These electrons originate in the magnetosphere, the region of space controlled by Earth’s magnetic field.As they rain into the atmosphere, the electrons impart energy to oxygen and nitrogen molecules, making them excited. When the molecules return to their normal state, they release photons, small bursts of energy in the form of light.

When billions of these collisions occur and enough photons are released, the oxygen and nitrogen in the atmosphere emit enough light for the eye to detect them.  This ghostly glow can light up the night sky in a dance of colors.  But since the aurora is much dimmer than sunlight, it cannot be seen from the ground in the daytime.

Young's Double Slit Experiment

This is a classic example of interference effects in light waves. Two light rays pass through two slits, separated by a distance d and strike a screen a distance, L , from the slits, as in Fig. 22.10.

Figure 22.10: Double slit diffraction

If d < < L then the difference in path length r1 - r2 travelled by the two rays is approximately:

r1 - r2 dsin

where is approximately equal to the angle that the rays make relative to a perpendicular line joining the slits to the screen.

If the rays were in phase when they passed through the slits, then the condition for constructive interference at the screen is:

dsin = m ,m = 1, 2,...

whereas the condition for destructive interference at the screen is:

dsin = (m + ) ,m = 1, 2,...

The points of constructive interference will appear as bright bands on the screen and the points of destructive interference will appear as dark bands. These dark and bright spots are called interference fringes. Note:
In the case that y , the distance from the interference fringe to the point of the screen opposite the center of the slits (see Fig.22.10) is much less than L ( y < <L ), one can use the approximate formula:

sin y/Lso that the formulas specifying the y - coordinates of the bright and dark spots, respectively are:

y Bm = brightspots

y Dm = darkspotsThe spacing between the dark spots is

y =

If d < < L then the spacing between the interference can be large even when the wavelength of the light is very small (as in the case of visible light). This give a method for (indirectly) measuring the wavelength of light. 

The above formulas assume that the slit width is very small compared to the wavelength of light, so that the slits behave essentially like point sources of light.

Common Emitter Transistor Amplifier

The larger collector current IC is proportional to the base current IB according to the relationship IC =βIB , or more precisely it is proportional to the base-emitter voltage VBE . The smaller base current controls the larger collector current, achieving current amplification.

The analogy to a valve is sometimes helpful. The smaller current in the base acts as a "valve", controlling the larger current from collector to emitter. A "signal" in the form of a variation in the base current is reproduced as a larger variation in the collector-to-emitter current, achieving an amplification of that signal.

The larger collector current IC is proportional to the base current IB according to the relationship IC =βIB , or more precisely it is proportional to the base-emitter voltage VBE . The smaller base current controls the larger collector current, achieving current amplification.

What is a mirage? How is it formed?

A traveller has lost his way in the desert. Enduring thirst and hunger, he suddenly saw an oasis, so the overjoyed man quickly ran towards it. To his great disappointment, it was just an illusion produced by a mirage. Such an episode was often pictured in movies, yet the optical magic that the nature plays with us - mirage - really exists in reality. Its formation is a result of the refraction and the total internal reflection of light in the air.

To investigate the formation of a mirage, we firstly need to understand why light is refracted in the air. Regions of air at different temperatures have different refractive indexes, just like many different mediums. The closer the air is to the ground, the hotter it will be, and its refractive index will be smaller. We could imagine the air as many layers of medium with a particular refractive index for every layer, and the refractive index is smaller for those that are closer to the ground. Thus when light travels in air, its path is as shown.

Vivax Solution

On the other hand, we should also understand what total internal reflection is. If light travels from glass to the air with a small incident angle, part of the light will be reflected back while the remaining part will be refracted, passing out from the glass. As the refractive index of glass is larger than that of the air, the refracted angle is always larger than the incident angle (Fig. 2). When the incident angle becomes larger, the refracted light will get closer and closer to the interface between the air and the glass. When it is larger than the critical angle, the light will only be reflected but not refracted. This phenomenon is called total internal reflection .

Suppose there is an oasis and the light it emits at point A is refracted by the air, the light will travel through a curved path. Total internal reflection occurs at point B and will cause the light to travel upwards. Then the light is refracted by the air again. At last, it will enter the eyes of the observer at point C, producing an illusion that the oasis is close to him.

Total internal reflection has been discovered for a long time already. Some of its broad applications include optical fibre, single lens reflex camera and binocular telescope.

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.

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.

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