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Electromagnetic Induction
FARADAY’S EXPERIMENT
The following experiments performed by Faraday led to the discovery of the phenomenon of electromagnetic induction :
Experiment 1. When the strength of magnetic field is varied. Consider two coils P and S wound on an iron rod. A battery and a tapping key K are connected to the coil P, while a sensitive galvanometer is connected to the coil S [Fig. ].
Faraday observed that deflection is produced in the galvanometer, when the tapping key K is pressed. When the tapping key is released, deflection is again produced but the direction of deflection is opposite. The galvanometer does not show any deflection, when the tapping key is kept pressed.
Explanation. When current flows through the coil P, magnetic field is produced along the axis of the coil. Since the coil S is wound on the same iron rod, magnetic flux gets linked with this coil also.
When the tapping key is just pressed, the current through coil P starts growing and it leads to a growing magnetic field through the coil S. As the magnetic flux linked with the coil S is changing (increasing), induced current is produced. On the other hand, when the key is released, the current through the coil P starts decaying. It results in decaying magnetic field through the coil S i.e. the magnetic flux linked with the coil S again starts changing (decreasing). Due to this, induced current is produced in the coil. Since the induced current is produced due to decaying magnetic field (earlier, the magnetic field was growing), the flow of current and hence the deflection in the galvanometer is in the opposite direction.
When the tapping key is kept pressed, the current in coil P becomes steady and hence magnetic flux linked with the coil S also becomes steady. Since induced current is produced only when the magnetic flux linked with the coil changes, the galvanometer does not show any deflection when the tapping key is kept pressed. -
Electromagnetic Induction
Experiment 2. When the source of magnetic field is moved towards or away from a stationary coil.
Consider a coil P wound on an iron rod and connected to a battery .A steady current flowing through the coil will produce a steady field along its axis. Another coil S having a galvanometer in its circuit is placed in line with the coil P [Fig.].
Faraday observed that deflection is produced in the magnetic galvanometer, when the coil P is moved towards the coil,S. If the coil P is moved away the galvanometer shows a deflection again, but this time, the deflection is in coil P is opposite direction. The deflection is produced in the galvanometer, only when the coil P is moved towards or away from the coil S
Explanation. When a steady current is passed through the coil P wound on an iron rod, the iron rod becomes an electromagnet. Since magnetic field lines crowd near the poles of the magnet, the magnetic flux linked with the coil S grows.When the coil P is moved towards the coil S; and decays when it is moved away. Since due to motion of the coil P towards or away from the coil S, the magnetic flux linked with coil S changes, the galvanometer shows deflection due to the flow of induced current in the coil S. In case the coil P is kept stationary, the magnetic flux linked with the coil S remains same and hence galvanometer does not show a
any deflection.
The same effects will be observed, if the electromagnet (the current carrying coil P wound on the iron rod) is replaced by a bar magnet NS [Fig. ].
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Electromagnetic Induction
Experiment 3. When a coil is moved in a stationary magnetic field.
Consider that a coil ABCD having a galvanometer G in its circuit is placed inside a uniform magnetic field, which is confined to the region PQRS only. The cross-marks indicate that the magnetic field is directed perpendicularly into the plane of the paper. When the coil is moved so that it remains entirely inside the magnetic field
the galvanometer does not show any deflection. On the other hand, when the coil is pulled out of the magnetic field (moved so that a part of the coil is inside the magnetic field and a part outside) as shown in Fig. , the galvano-meter shows deflection.
Explanation. When the coil is moved entirely inside the magnetic field [Fig. ], the magnetic flux linked with its area ABCD does not change. Due to this, no induced current is produced in the coil and the galvanometer does not show any deflecdeflection.
However, when the coil is moved as shown in Fig. 1.08, the area of the coil inside the magnetic field goes on decreasing i.e. the magnetic flux linked with the coil goes on decreasing. As a result, the induced current flows through the coil and the galvanometer shows deflection. The e.m.f. so produced in the coil is called motional e.m.f. It is a consequence of Lorentz magnetic force on the electrons inside the wire, of which the coil is made of. However, the expression for motional e.m.f. can be obtained both by finding Lorentz magnetic force on the electrons inside the wire forming the coil and by applying Faraday's law of electromagnetic induction. -
Electromagnetic Induction
FARADAY’S LAWS OF ELECTROMAGNETIC INDUCTION
The results of Faraday's experiments on electromagnetic induction are known Faraday's laws of electromagnetic induction. These laws are stated as below:
1. Whenever magnetic flux linked with a circuit (a loop of wire or a coil or an electric circuit in general) changes, induced e.m.f. is produced.
2. The induced e.m.f. lasts as long as the change in the magnetic flux continues. 3. The magnitude of the induced e.m.f. is directly proportional to the rate of change of the magnetic flux linked with the circuit
Let \(\phi_1\) and \(\phi_2\) be the values of magnetic flux linked with the coil initially at t=0) and at time t respectively. Then,
rate of change of magnetic flux= \( \frac{{\phi _2 - \phi _1 }} {t} \)
If e is the induced e.m.f. produced, then
\(e\alpha \frac{{\phi _2 - \phi _1 }} {t} \)
or e= -k \( \frac{{\phi _2 - \phi _1 }} {t} \)
Here, k is the constant of proportionality and the negative sign indicates that the induced e.m.f. has got opposing nature i.e. direction of flow of current due to the induced e.m.f. is such that it opposes the change in magnetic flux. In SI, the constant of proportionality* is 1. Hence,
\( e = - \frac{{\phi _2 - \phi _1 }} {t} \) ...........(5)
In SI, e is measured in volt,\(\phi\) in weber and t in second
If \(d\phi\) is small change in magnetic flux in a small time dt, then the equation (5) may be expressed as
\( e = - \frac{{d\phi }} {{dt}} \) ..........(6)
The equation (5) or (6) can be used to find the induced e.m.f. produced in a coil due to change in magnetic flux linked with the coil.
If the coil consists of N turns, then magnetic flux equal to p is linked with each turn of the coil. Hence,
the total magnetic flux linked with the coil = N \(\phi\)
Therefore, induced e.m.f. produced in the coil,
\( e = - \frac{d} {{dt}}\left( {N\phi } \right)\)
or \( e = - N\frac{{d\phi }} {{dt}}\) ..........(7)
The equation (6) or (7) is commonly known as Faraday-Lenz's law. -
Electromagnetic Induction
LENZ’S RULE
Lenz's rule is a convenient method to determine the direction of induced current produced in a circuit. It is related to the principle of conservation of energy and it accounts for the negative sign appearing in equation (1.06) or (1.07).
Lenz's law states that the induced current produced in a circuit always flows in such a direction that it opposes the change or the cause that produces it.
Let us now apply Lenz's rule to find the direction of flow of induced current in the Faraday’s experiments.
Experiment 1. Refer to Fig. . On pressing the key K, the current in the coil P flows in clockwise direction, when seen from left and the magnetic field lines so produced will be directed from left to right. As the current grows through the coil P, the magnetic flux will also grow through the coil S. The direction of flow of induced current in coil S should be such that it opposes the growth of magnetic flux through it. The growing magnetic flux will be opposed, if the induced current in the coil S produces magnetic field lines from right to left. Consequently, the induced current in the coil S should flow in anticlockwise direction, when seen from left. -
Electromagnetic Induction
FLEMING’S RIGHT HAND RULE
We know that when a conductor is moved inside the magnetic field in a direction perpendicular to the direction of magnetic field, induced e.m.f. is produced across its two ends. The direction of flow of current can be found by applying Lenz's rule.
The direction of flow of the induced current can also be found by applying Fleming's right hand rule, when the direction of motion of conductor inside the magnetic field and the direction of magnetic field acting on it are known.
Fleming's right hand rule. It states that if the thumb, fore finger and the central finger of the right hand are kept perpendicular to each other [Fig.], so that the fore finger points in the direction of the field and the thumb in the direction of motion of the conductor, then the induced current flows in the direction of the central finger.
