# Back Emf in a Motor

Gear300
Say you had a circuit with a battery and a loop of wire somewhere in the middle of the circuit. The loop of wire is positioned so that it is free to rotate in a uniform magnetic field, and since a current is running through it, a torque will be supplied by the magnetic force allowing it to rotate. The rotation of the coil will cause a changing magnetic flux because the angle constantly changes. The circuit to begin with was a DC circuit, but if an expression were to be derived for the emf induced in the coil, it would be an alternating emf. Does the back emf alternate back and forth completely or does it only vary sinousidally every half a period much like the emf provided in DC generators?

Staff Emeritus
Homework Helper
It should alternate + and - similar to a sine wave.

When the torque on the coil is in the direction it is rotating, the back-emf is negative as in a DC motor, and current is reduced.
When the torque opposes the direction of rotation (i.e. it is being decelerated), the emf is positive, and current is increased.

Hope that helps.

p.s. I'm not sure if or how the changes in current would make the oscillations deviate from a true sine wave (it's getting late and it's been a while since I thought about this stuff).

Gear300
I see...I was thinking that it was a sine wave, but one that didn't alternate so that it would increase the current (meaning that half the period would be cut off per cycle...sort of like the absolute value of the sine function instead).

Homework Helper
Gold Member
Er, it will move but it will not rotate, it will position itself so that the N field of the coil points to the S pole of your magnet or vice versa, and stay like that till you switch current off. To get rotation you have now to change the direction of one of the magnetic fields somehow. That is the whole engineering question for how to make electric motors I think.

Staff Emeritus