The Open Door Web Site
Electricity and Magnetism

EMF Induced in a Conductor Moving through a Magnetic Field

A conductor is moved a distance, Ds, at 90° to a magnetic field of flux density B, in time Dt.

The free electrons in the conductor will experience a force causing them to move through the conductor. Suppose that a total charge DQ moves past any point in the conductor in time Dt.

The work done by the force F is given by

w = FDs

This work is equal to the energy given to the charge DQ.

Therefore, the work done per unit charge is

and, work done per Coulomb is the induced emf .

Therefore

 

 

If the conductor moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current, I, induced in it.

Therefore,

so

which gives

 

© David Hoult 2008