Motional Electromotive Force

The current induced in the wire is due to the motion of the wire through the magnetic field. According to Faraday's law, the induced emf (

%5Cepsilon

) is given by:

%5Cepsilon%20%3D%20BvL

Where

v

is the velocity of the wire as it falls under the influence of gravity. Using the equation

v%5E2%20%3D%202gL

, the velocity is:

v%20%3D%20%5Csqrt%7B2gL%7D

Thus, the induced emf becomes:

%5Cepsilon%20%3D%20B%5Csqrt%7B2gL%7DL

The current

I

is given by Ohm's law:

I%20%3D%20%5Cfrac%7B%5Cepsilon%7D%7BR%7D%20%3D%20%5Cfrac%7BB%5Csqrt%7B2gL%7DL%7D%7BR%7D

Thus, the induced current is:

I%20%3D%20%5Cfrac%7BBL%5Csqrt%7B2gL%7D%7D%7BR%7D

Chapter Questions
1 MCQs