Energy Consideration: A Quantitative Study
we discussed qualitatively that Lenz’s law is consistent with the law of conservation of energy. Now we shall explore this aspect further with a concrete example.
Let r be the resistance of movable arm PQ of the rectangular conductor.
We assume that the remaining arms QR, RS and SP have negligible resistances compared to r.
Thus, the overall resistance of the rectangular loop is r and this does not change as PQ is moved.
The current I in the loop is
I = έ/r
=Blv/r
On account of the presence of the magnetic field, there will be a force on the arm PQ.
This force I(l××B), is directed outwards in the direction opposite to the velocity of the rod.
The magnitude of this force is F = IlB = B2l2v/r
the arm PQ is being pushed with a constant speed v,
the power required to do this is P = Fv B2l2v2/r