# Current on a DC motor

we have a magnet, a dc source, and a circular winding that has little length but a lot of turns. Now, if we were to hold the winding so that It can not turn due to lorentz force and so there will be no induced EMF, In that case Lewin says there would be huge amount of current drawn from the DC source. But if we free the winding so that winding would turn freely, current drawn from the source will be 40 times smaller than the first case.

My question is, when I tried to write down the equation I couldn't come up with the same result. Here is my calculations:

B:magnetic field of the magnet on the winding(assumed to be constant)

A: area of circle

N: number of turns

Q: angle between the surface normal of the winding and magnetic field

Rs: resistance of the source

Vs: voltage of the source

note: winding has also resistance but it is neglected

1. -(magnetic flux change)= EMF= B.A.N.sinQ
2. closed line integral of Electric field of the circuit = B.A.N.sinQ= I.Rs-Vs

according to "2)" current drawn from the source must oscillate within the range that also includes the case where the winding is not allowed to turn. If to simplify, for the first case , if the current is 30 ampere for the second case, it must oscillate between 20 ampere and 40 ampere. Because magnetic field is hugely dependent on the magnet unlike if there were no magnet.