Motional EMF

Motional EMF

Motional emf is the emf induced in any conductor of any shape which is moving in any magnetic field assuming that the magnetic field at each point does not vary with time.

ε = -Blv

Assume a straight rod or a conductor is moving perpendicular in direction with a constant velocity and external driving force. The electrons present in a conductor face a force

along the length of the conductor which is perpendicular to velocity

and the magnetic flux

. Due to this force the electrons move to the lower end of the conductor and added with each other. The electric field

is produced inside the conductor so that the electrons are added on both ends of the conductor and these electrons are added with each other till the downward magnetic force

is balanced with the upward magnetic force qe

So, the force for balancing the electrons on both ends is:

Then the electric field is produced in a conductor so the potential difference

So, the balancing equation is

If the direction of the motion of the conductor is reversed then the potential difference will also be reversed.

Assume a circuit which consists of a conducting bar of length l is placed perpendicular along the two parallel rails and these rails are connected to the resistor in series on the other end. The magnetic field

is functioned on the circuit perpendicularly. The bar has zero resistance and it is pulled to right with velocity due to applied force and the charges starts moving in the magnetic field which bears a magnetic force along the length of the conducting bar. The magnetic flux of the circuit and the produced motional EMF becomes proportional to each other with the area of the circuit.

The area of the circuit is lx where l is the length of the conducting bar and x is the position of the magnetic bar thus the magnetic flux through the area is: