Question 6: What is motional emf? Show that motional induced emf = Blv.
Definition of Motional emf
“Motional emf is the emf induced by the motion of the conductor across a magnetic field.”
Explanation of Motional emf
Consider a conductor MN of length l moving in a magnetic field B as shown in the figure. In this arrangement, the conductor is part of a closed circuit. A galvanometer is provided in the circuit. When the conductor is stationary, the galvanometer shows no deflection (that is no current flow). When the conductor is moved to left or right, the galvanometer shows a deflection.
Let we move the conductor to the left with a constant velocity v. The charged particle q in the conductor experiences a force = q(vxB) . [See equation 13.7 of your textbook, “Motion of charged particle in uniform magnetic field”].
Again the force on the conductor, as it is carrying a current, is F = BIl . [See section 13.2 of your textbook, “Force on a current carrying conductor]. The direction of this force can be found by applying Fleming’s Left Hand Rule. We see this force is directed to the right; opposite to the applied force. So we conclude the applied force is doing work against the magnetic force given in the above equation.
As rate of work done is power, therefore, the power of the applied force is BIlv .
Now if ε is the electromotive force induced, then the electrical power is
Now according to the principle of conservation of energy, the rate of work done is equal to the rate of production of electrical energy. Therefore,
This is the required expression.
Please note that in this case the B, l and v are perpendicular to one another. In case L and B are making an angle θ with one another then we take the component of B which is perpendicular to L.