# 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 forceon the arm PQ. This force
I(l××B), is directed outwards in the directionopposite to the velocity of the rod. The magnitude of this force is
F = IlB = B^{2}l^{2}v/r
the arm PQ is being pushed with a constant speed v,the power required to do this is P = Fv B^{2}l^{2}v^{2}/r