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# Classwork Exercise and Series (Physics- SS3): Electromagnetic Induction

Introduction To Electromagnetic Induction

The term electromagnetic induction refers to the generation of an electric current by passing a metal wire through a magnetic field. The discovery of electromagnetic induction in 1831 was preceded a decade earlier by a related discovery by Danish physicist Hans Christian Oersted (1777–1851). Oersted showed that an electric current produces a magnetic field. That is, if you place a simple magnetic compass near any of the electrical wires in your home that are carrying a current, you can detect a magnetic field around the wires. If an electric current can produce a magnetic field, physicists reasoned, perhaps the reverse effect could be observed as well. So they set out to generate an electric current from a magnetic field.

That effect was first observed in 1831 by English physicist Michael Faraday (1791–1867) and shortly thereafter by American physicist Joseph Henry (1797–1878). The principle on which the Faraday-Henry discovery is based is shown in the figure on page 762. A long piece of metal wire is wound around a metal bar. The two ends of the wire are connected to a galvanometer, an instrument used to measure electric current. The bar is then placed between the poles of a magnet.

Electric current: A flow of electrons.

Electrical generator: A device for converting mechanical (kinetic) energy into electrical energy.

Galvanometer: An instrument used to measure the flow of electric current.

Potential difference: Also called voltage; the amount of electric energy stored in a mass of electric charges compared to the energy stored in some other mass of charges.

Transformer: A device that transfers electric energy from one circuit to another circuit with different characteristics.

As long as the bar remains at rest, nothing happens. No current is generated. But moving the bar in one direction or another produces a current that can be read on the galvanometer. When the bar is moved downward, current flows in one direction through the metal wire. When the bar is moved upward, current flows in the opposite direction through the wire. The amount of current that flows is proportional to the speed with which the wire moves through the magnetic field. When the wire moves faster, a larger current is produced. When it moves more slowly, a smaller current is produced.

Actually, it is not necessary to move the wire in order to produce the electric current. One could just as well hold the wire still and move the magnetic poles. All that is necessary is the creation of some relative motion of the wire and the magnetic field. When that happens, an electric current is generated.

Applications

Many electrical devices operate on the principle of electromagnetic induction. Perhaps the most important of these is an electrical generator. An electrical generator is a device for converting kinetic energy (the energy of an object due to its motion) into electrical energy. In a generator, a wire coil is placed between the poles of a magnet and caused to spin at a high rate of speed. One way to make the coil spin is to attach it to a turbine powered by water, as in a dam. Steam from a boiler can also be used to make the coil spin.

As the coil spins between the poles of the magnet, an electric current is generated. That current then can be sent out along transmission lines to homes, office buildings, factories, and other consumers of electric power.

Induced Current

This involves generating a voltage by changing the magnetic field that passes through a coil of wire.

First, connect a coil of wire to a galvanometer, which is just a very sensitive device we can use to measure current in the coil. There is no battery or power supply, so no current should flow. Now bring a magnet close to the coil. You should notice two things:

If the magnet is held stationary near, or even inside, the coil, no current will flow through the coil.

If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil. When the magnet is moved one way (say, into the coil), the needle deflects one way; when the magnet is moved the other way (say, out of the coil), the needle deflects the other way. Not only can a moving magnet cause a current to flow in the coil, the direction of the current depends on how the magnet is moved.

How can this be explained? It seems like a constant magnetic field does nothing to the coil, while a changing field causes a current to flow.

To confirm this, the magnet can be replaced with a second coil, and a current can be set up in this coil by connecting it to a battery. The second coil acts just like a bar magnet. When this coil is placed next to the first one, which is still connected to the galvanometer, nothing happens when a steady current passes through the second coil. When the current in the second coil is switched on or off, or changed in any way, however, the galvanometer responds, indicating that a current is flowing in the first coil.

You also notice one more thing. If you squeeze the first coil, changing its area, while it’s sitting near a stationary magnet, the galvanometer needle moves, indicating that current is flowing through the coil.

What you can conclude from all these observations is that a changing magnetic field will produce a voltage in a coil, causing a current to flow. To be completely accurate, if the magnetic flux through a coil is changed, a voltage will be produced. This voltage is known as the induced e.m.f.

The magnetic flux is a measure of the number of magnetic field lines passing through an area. If a loop of wire with an area A is in a magnetic field B, the magnetic flux is given by:

ɸ = BA cosɸ, where ɸ is the angle between the magnetic field B and vector A, which is perpendicular to the plane of the loop.

If the flux changes, an emf will be induced. There are therefore three ways an e.m.f. can be induced in a loop:

Change the magnetic field

Change the area of the loop

Change the angle between the field and the loop

Factors affecting the magnitude of the induced E.M.F.:

When a magnet is pushed into a coil as shown, the galvanometer deflects in one direction momentarily.

When the magnet is not moving, the galvanometer shows no reading.

When the magnet is withdrawn from the coil, the galvanometer deflects in the opposite direction momentarily.

The magnitude of the deflection depends on the magnetic field density B, the speed of motion v of the magnet, and the number of turns N in the coil.

An e.m.f. can be induced in a coil if the magnetic flux through the coil is changed. It also makes a difference how fast the change is; a quick change induces more e.m.f. than a gradual change. This is summarized in Faraday’s law of induction. The induced e.m.f. in a coil of N loops produced by a change in flux in a certain time interval is given by:

Faraday’s law of Induction: ɛ = -N∆ɸ/∆t

Recalling that the flux through a loop of area A is given by

ɸ = BA cosɸ,

ɛ = -N∆ (BA cosɸ)/∆t

The negative sign in Faraday’s law comes from the fact that the e.m.f. induced in the coil acts to oppose any change in the magnetic flux. This is summarized in Lenz’s law.

Lenz’s law: The induced emf generates a current that sets up a magnetic field which acts to oppose the change in magnetic flux.

Another way of stating Lenz’s law is to say that coils and loops like to maintain the status quo (i.e., they don’t like change). If a coil has zero magnetic flux, when a magnet is brought close then, while the flux is changing, the coil will set up its own magnetic field that points opposite to the field from the magnet. On the other hand, a coil with a particular flux from an external magnetic field will set up its own magnetic field in an attempt to maintain the flux at a constant level if the external field (and therefore flux) is changed.

An example

Consider a flat square coil with N = 5 loops. The coil is 20 cm on each side, and has a magnetic field of 0.3 T passing through it. The plane of the coil is perpendicular to the magnetic field: the field points out of the page.

(a) If nothing is changed, what is the induced e.m.f.?

There is only an induced e.m.f. when the magnetic flux changes, and while the change is taking place. If nothing changes, the induced e.m.f. is zero.

(b) The magnetic field is increased uniformly from 0.3 T to 0.8 T in 1.0 seconds. While the change is taking place, what is the induced e.m.f. in the coil?

Probably the most straight-forward way to approach this is to calculate the initial and final magnetic flux through the coil.

Initial magnetic flux: ɸ0 = B0A = 0.3 (0.2)2 = 0.012Tm2

Final magnetic flux: ɸf = BfA = 0.8 (0.2)2 = 0.032Tm2

The induced e.m.f. is then:

ɛ = -N∆ɸ/∆t = -N (ɸf – ɸ0)/∆t = -5 (0.032 – 0.012)/1.0 = -0.1v

(c) While the magnetic field is changing, the e.m.f. induced in the coil causes a current to flow. Does the current flow clockwise or counter-clockwise around the coil?

To answer this, apply Lenz’s law, as well as the right-hand rule. While the magnetic field is being changed, the magnetic flux is being increased out of the page. According to Lenz’s law, the emf induced in the loop by this changing flux produces a current that sets up a field opposing the change. The field set up by the current in the coil, then, points into the page, opposite to the direction of the increase in flux. To produce a field into the page, the current must flow clockwise around the loop. This can be found from the right hand rule.

One way to apply the rule is this. Point the thumb on your right hand in the direction of the required field, into the page in this case. If you curl your fingers, they curl in the direction the current flows around the loop – clockwise.

Fleming’s Right Hand Rule

The rule states that, if our right hand is held so that the thumb, the forefinger and the middle finger are perpendicular to one another, the thumb will represent the direction of motion in the conductor, the fore finger will represent the direction of the magnetic field, while the middle or second finger will represent the direction of the induced current. The difference between Fleming’s right hand and left hand rule is that the right hand rule is used for induced current or e.m.f. while the left hand refers to the force in the conductor.

Induction Coil

Induction Coil, a device for converting low-voltage direct current (DC) into high-voltage alternating current (AC). The coils are used chiefly in the electrical systems of automobiles and to operate X-ray tubes.

A typical induction coil has a core of soft iron, a primary coil, and a secondary coil. The primary coil consists of a few turns of fairly heavy wire around the core; the secondary consists of many turns of fine wire around the primary. The primary coil forms part of a circuit called the primary circuit that includes a direct current source and a circuit breaker, or interrupter.

When the primary circuit is closed, direct current flows through the primary coil, producing a magnetic field. As the magnetic field builds up, it induces an electric current in the secondary coil. At the same time, the iron core becomes magnetized. The magnetized core draws the interrupter away from a metal contact, breaking the primary circuit. The direct current in the primary coil ceases and the coil’s magnetic field collapses, again inducing an electric current in the secondary coil, only in the opposite direction. Simultaneously, the core loses its magnetism and releases the interrupter, which is pulled back against the contact by a spring. The cycle continues to repeat rapidly, supplying an alternating current at the terminals of the secondary coil. The voltage in the secondary coil is higher than in the primary coil because of the greater number of turns in the secondary coil.

A capacitor, or condenser, is often used with an induction coil. The capacitor prevents sparking between the interrupter and contact by briefly storing the electric charge that would otherwise jump the gap between them.

Principle

AC Dynamo is based on the phenomenon of electromagnetic induction. That is, when the relative orientation between the coil and the magnetic field changes, the flux linked with the coil changes and this induces a current in the coil.

As the armature coil rotates, the angle Q changes continuously. Therefore, the flux linked with the coil changes.

Now, ɸ = N(B.A)

= NBA cos q

= NBA cos wt

where q is the flux linked with the coil, N is the number of turns in the coil, A is the area enclosed by each three of the coil and B is the strength of the magnetic field.

E = -dɸ/dt = – d(NBA cos wt)/dt   (from Faraday’s law of EMF)

= – NBA (-sin wt )w

E = + NBA w sin wt

e = eo sinwt. This is the EMF Supplied by the A.C. generator

i = ɛ/R = ɛ0/R sin ωt = i0 sin ωt

Armature

ABCD is the armature coil consisting of a large number of turns of the insulated copper wire wound over a laminated soft iron core I. The coil can be rotated about the central axis.

Magnets

N and S are the pole pieces of a strong electromagnet in which the armature coil is rotated.

Slip rings

R1 and R2 are two hollow metallic rings to which both ends of the armature coil are connected. These rings rotate with the rotation of the coil.

Brushes

Brushes B1 and B2 are two flexible metal plates or carbon rods. These brushes are used to pass current from the coil to the external load resistance.

Working

To start with, suppose the plane of the coil is perpendicular to the plane of the paper in which the magnetic field is applied, with AB at the front and CD at the back, the flux linked with the coil is maximum in this position. As the coil rotates clockwise, AB moves inwards and CD moves outwards. According to Fleming’s right hand rule, the current induced in AB is from A to B, and in CD, from C to D. In the external circuit, current flows from B2 to B1. After half of the rotation of the coil, AB is at the back and CD is at the front. Therefore, AB starts moving outwards and CD inwards. The current induced in AB is from B to A, and in CD, from D to C. The current flows from B1 to B2 through the external circuit. We therefore see that the induced current in the external circuit changes direction after every half rotation of the coil, and hence is alternating in nature.

Alternator is an electric generator which changes the position or direction of flow of voltage and current. The current that changes is called the alternating current.

Transformers and Power transmission Distribution

Transformers also operate on the principle of electromagnetic induction. Transformers are devices that convert electric current from one potential difference (voltage) to another potential difference. For example, the current that comes from a power plant is typically high voltage current, much higher than is needed or than can be used in household appliances. A step-down transformer uses electromagnetic induction to convert the high voltage current in power lines to the lower voltage current needed for household appliances.

We have already seen that a change in flux induces an emf in a coil, given by Faraday’s Law:

ɛ = – N dɸ/dt

We have also seen that a voltage in a coil induces a magnetic flux inside the coil. If we were to connect two coils with the same core, the flux, and the rate of change of flux, would be exactly the same inside both coils. We would have created a kind of flux circuit known as a transformer. The ratio between the voltage at the primary coil Vp and the voltage at the secondary coil Vs would have to be (since φ is constant):

VP/Vs = -Np /dt / -Ns /dt = Np/Ns,

where Np and Ns are the numbers of coils in the primary and secondary coils respectively.

In other words, we can change the voltage of some electricity by varying the number of coils in each coil. In order for this to work, the current used must be an alternating current (AC). This means that the current and voltage are constantly changing sinusoidally, and so there is a sinusoidal change in flux. This means that an e.m.f. is induced in the secondary coil. If the flux did not change (i.e. we were using direct current), then no e.m.f. would be induced, and the transformer would be useless except as a magnet (since it would still have a flux circuit in it).

Ideal Transformers

An ideal transformer is one in which all the electrical energy put into one coil comes out of the other coil. An ideal transformer does not exist, but, since it makes the maths easy, we like to pretend that it does. In this case, the power in must equal the power out:

P = Pp = Ps = Ip Vp = Is Vs,

where Ip and Is are the currents in the primary and secondary coils, respectively. So:

Vp = P/Ip and Vs = P/Is

By substitution into the transformer equation for voltage:

Ns/Np = Vs/Vp = P/Is /P/Ip = /1/Is /1/Ip = Ip/Is

Ns/Np = Vs/Vp = Ip/Is

So, in an ideal transformer, the ratio between the voltages is equal to the ratio between the numbers of coils, but the ratio between the currents is equal to the reciprocal of the ratio between the numbers of coils.

Mutual Inductance is the flow of induced current or voltage in a coil due to an alternating or varying current in a neighbouring coil.

Eddy Currents

In reality, the electrical energy is not all conserved, a lot of it is converted into heat by eddy currents. In a transformer, the magnetic flux created by the primary coil induces a current in the core. This occurs in order to oppose the change that produced the magnetic flux (Lenz’s Law). The currents flowing in the core are called eddy currents.

These currents produce heat, using up energy and so causing inefficiency. One way of minimizing the effects of eddy currents is to make the core out of iron laminate. This is layers of iron separated by thin layers of an insulator such as varnish. The amplitude of the eddy currents produced is reduced as currents cannot flow through the layers of insulator.

Hysteresis Loss is wasted energy due to reversing the magnetization of core. The core is made to go through a cycle of magnetization during each alternating cycle of the primary current. Hysteresis loss is reduced by the use of special alloys in the core of the primary coil, or by the use of soft iron cores.

I2 R (or Heat) Loss because the primary and secondary coils have resistance, some energy is lost in the form of heat (I2 R) in the coils. This heat loss can be reduced by using thick wires, or low resistance coils.

Leakage of Magnetic Flux

Some energy is lost due to leakage of magnetic flux. This arises because not all the lines of induction due to current in the primary coil pass entirely through the iron core. This loss is reduced by special forms of coil winding, or by efficient core design.

It is because of the above losses that the efficiency of practical transformer is less than 100%.

The efficiency of a transformer is defined by

Efficiency = Output Power/Input Power x 100% = Power in the secondary coils/Power in the primary coils x 100%

Example

1. Find the turns ration in a transformer which delivers a voltage of 120 volts in the secondary coil from a primary voltage of 60 volts.

Solutions

Turns ratio = Ns/Np

Es/Ep = Ns/Np

120/60 = Ns/Np = 2

Turns ratio = 2

2. A magnetic field of flux density 20 T passes down through a coil of wire, making an angle of 60° to the plane of the coil as shown. The coil has 500 turns and an area of 25 cm2. Determine:

 (i) the magnetic flux through the coil φ = B A sin ɸ = 20 (sin 60°) 25 x 10-4 = 0.0433 Wb

(ii) the flux linkage through the coil
Φ = N φ
= 500 x 0.0433 = 21.65 Wb

Questions:
1. An ideal transformer transforms a 50A current into a 1A current. It has 40 coils on the primary coil. How many coils are in the secondary coil?

A. 5.1 KV B. 6.2 KV C. 7.3 KV 4. 8.4 KV

2. A step-down transformer has 300 coils on one coil, and 50 coils on the other. If 30 kV AC is put in, what voltage comes out?

A. 6 KV B. 5 KV C. 4 KV D. 3.5 KV

3. A magnetic field of flux density 20 T passes down through a coil of wire, making an angle of 60° to the plane of the coil as shown. The coil has 500 turns and an area of 25 cm2.

Determine the magnetic flux through the coil

A. 0.786 Wb B. 0.0433 Wb C. 1.434 Wb D. 0.434 Wb

4. Which of these statements is not correct?

A. The magnetic flux is a measure of the number of magnetic field lines passing through an area.

1. When a magnet is pushed into a coil as shown, the galvanometer deflects in one direction momentarily.

C. In a transformer, the magnetic flux created by the primary coil induces a current in the core.

D. because the primary and secondary coils have resistance, some energy is lost in the form of heat (I2 R) in the coils. This heat loss can be reduced by using flexible wires.

5. What year did the English physicist Michael Faraday observed the electromagnetic induction effect?

A 1830   B. 1831   C. 1832   D. 1833