As soon as Oersted discovered that electric currents produce magnetic fields,many scientist began to look for the reverse effect, that is, to cause an electric current by means of a magnetic field. In 1831 Michael Faraday in England and at the same time Joseph Henry in USA observed that an emf is set up in a conductor when it moves across a magnetic field. If the moving conductor were connected to a sensitive galvanometer, it would show an electric current following through the circuit as the conductor is kept moving in the electric field. The emf produced in the conductor is called induced emf, and the current generated is called the induced current. This phenomenon is known as electromagnetic induction.
Induced EMF and Induced Current:
There are many ways to produced induced emf figure illustrated one of them. Consider a straight piece of wire of length l placed in the magnetic field of a permanent magnet. The wire is connected to a sensitive galvanometer. This forms a closed path or loop without any battery. In beginning when the loop is at rest in the magnetic field, no current is shown by the galvanometer. If we move the loop from the left to right, the length l of the wire is dragged across the magnetic field and a current follows through the loop. As stop moving the loop, current also stops. Now, if we move the loop in opposite direction, current also reverses its direction. This is indicated by the deflection of the galvanometer opposite direction.
The induced current depends upon the speed with which conductor moves and upon the resistance of the loop. If we change the resistance of the loop by inserting different resistors in the loop, and it in the magnetic field with the same speed every time, we find that the product of induced current I and the resistance R of the loop remains constant,i.e.,
I×R = constant
This statement is the induced emf. This induced emf leads to an induced current when the circuit is closed. The current can be increased by
- Using a stronger magnetic field
- Moving the loop faster
- Replacing the loop by a coil of many turns
If we perform the above experiment in the other way i.e., instead of moving the loop across the magnetic field, we hold the loop stationary and move the magnet, then it can be easily observed that the results are the same. Thus, it can be concluded that it is the relative motion of the loop and the magnet that causes the included emf.
In fact, this relative motion changes the magnetic flux through the loop, therefore, if we say that an induced emf is produced in a loop if the magnetic flux through it changes. The greater the rate of change of flux, the larger is the induced emf.
There are some other methods described below in which an emf is induced in a loop by producing a change of magnetic flux through it.
Fig (a) shows a bar magnet and a coil of wire to which a galvanometer is connected. When there is no relative motion between the magnet and the coil, the galvanometer indicates no current in the circuit. As soon as the bar magnet is moved towards the coil, a current appears in it as shown in fig(b). In moving the magnet,the magnetic flux through the coil changes, and this changing flux produces the induced current in the coil. When the magnet moves away from the coil, a current is again induced but now in opposite direction. The current would also be induced if the magnets were held stationary and the coils were moved.
There is another method in which the current is induced in a coil by changing the area of the coil in a constant magnetic field. That no current is induced in the coil of constant area that is placed in a constant magnetic field. However, when the coil is being distorted so as to reduce its area, an induced emf and hence current appears. The current vanishes when the area is no longer changing. If the distorted coil is brought to its original circular shape thereby increasing the area, an oppositely directed current is induced which lasts as long as the area is changing.
An induced current can also be generated when a coil of constant area is rotated in a constant magnetic field. Here, also, the magnetic flux through the coil changes shows in above figure. This is the basic principle used in electric generators.
A very interesting method to induce current in a coil involves by producing a change of magnetic flux in a nearby coil.
Two coils placed side by side. The coil P is connected in series with a battery, a rheostat and a switch, while the other coil S is connected to a galvanometer only. Since there is no battery in the coil S, one might expect that the current through it will always be zero. Now, if the switch of the coil P is suddenly closed, a momentary current induced in coil S. This is indicated by the galvanometer, which suddenly deflects and the returns to zero. No induced current exits in coil S as long as the current flows steadily in the coil P. An oppositely directed current is induced in the coil S at the instant the switch of the coil P is opened. Actually, the current in P grows from zero to its maximum value just after the switch is closed. The current come down to zero when the switch is opened. Due to change in current, the magnetic flux associated with the coil P changes momentarily. This changing flux also linked with the coil S that causes the induced current in it. Current in coil P can also be changed with the help of rheostat.
It is also possible to link the changing magnetic flux with a coil by using an electromagnetic instead of a permanent magnet. The coil is placed in the magnetic field of an electromagnetic.
Both the coil and the electromagnet are stationary. The magnetic flux through the coil is changed by changing the current of the electromagnet, thus producing the induced current in the coil.
“The emf induced by the motion of a conductor across a magnetic field is called motional emf”.
In the previous section we have studied that when conductor is moved across a magnetic field, an emf induced between its ends. The emf of the moving conductor is similar to that of a battery,i.e., if the ends of the conductor are joined by a wire to make a closed circuit, a current flow through it.
Consider a conducting rod of length L placed on two parallel metal rails separated by a distance L. A galvanometer is connected between the ends c and d of the rails. This forms a complete conducting loop abcd. A uniform magnetic field B is applied directed into the paper. Initially,
When the rod is stationary, galvanometer indicates no current the loop. If the rod is pulled to the right with constant velocity v, the galvanometer indicates a current flowing through the loop. Obviously, the current is induced due to the motion of the conducting rod across the magnetic field. The moving rod is acting as a source E =Vb –Va = ∆V.
When the rod moves, a charge q within the rod also moves with the same velocity v in the magnetic field B and the experiences a force given by
F =qv × B
The magnitude of the force is:
F = qv B sinθ
Since angle θ between v and B is 90° ,so
F = q vB
Applying the right hand rule, we see that F is directed from a to b in the rod. This suggests a uniform electric field E is induced along the rod. Its magnitude is given by:
substituting F =q v B in equation E=F/q,we have:
E =vB ……..(1)
The direction of electric intensity is that of force F i.e., it is directed from a to b. As the electric intensity is given by negative of the potential gradient, therefore
E = -ΔV/L
Comparing equation (1) and (2) we get:
ε =-vBL ………..(3)
This is the magnitude of motional emf.However,if the angle between v and B is θ,then
ε =vBL sinθ ……….(4)
The above equation shows that when v=0,∑=0, that means no motional emf is developed in the stationary rod. It is also obvious that by increasing the speed of rod and using stronger field, emf can be increased.
Due to induced emf positive charges would flow along the path , therefore the induced current is anticlockwise the diagram.