# Motional Electromotive Force Formula

Motional Electromotive Force Formula

The magnetic force exerted on the charges in a moving conductor will generate a motion that can be associated with a voltage. The generated voltage can be seen to be the work done per unit charge.

Motional EMF = velocity of the charge carriers *Magnetic field * length of the wire

The equation is:

EMF = v B L

Where:

EMF: Electromotive force

v: Velocity of the charge

B: Magnetic field

L: Length of the wire where the charge is moving

EMF Formula Questions:

1) An electron is moving with a drift velocity into a wire of 1 m at 10 mm/h, if a magnetic field crosses and has B= 2 T. What is the EMF?

From the formula of the EMF,

EMF = v B L = 10 mm/h * 2 T * 1 m = 2.7*10(-6) m/s * 2 T * 1 m

EMF = 5.4*10(-6) m2 T/s = 5.4*10(-6) V

2) If a charge is moving in a wire of 1 m with a EMF of 2 V summited to a magnetic field B=2 T. What is it velocity?

From the formula of the EMF we find the velocity,

v = EMF/BL = 2 V/ ( 2 T * 1 m) = 1 V/Tm = 1 m/s

Φ = 5*10(-5) T m