“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.
Motional emf formula
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)
Motional emf equation
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.