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# Derive an expression for motional emf across a conductor moving in a magnetic field.

3 years ago

Arun
25211 Points

When a conductor is moved across a magnetic field, a potential difference is setup across its ends.
This potential difference is called'motional EMF'.

Consider a wire of length "L" moving across the magnetic field of inductionBwith a velocityvas shown in diagram.

Each free electron of the wire is moving within the wire and experience a force exerted by magnetic field.
$F=q(v\times B)$
here q=-e
$F=-e(v\times B)$
$F=e(B\times v)$

These electrons gradually accumulate at the end "a" and leaving the other end "b".In this way point "b" acquires positive charge and point "a" acquires equal negative charge.
This accumulation of electrons will continue till the force of electric field balances the force due to the motion of wire. Thus a potential difference is setup form pointbto pointa.

We know
Potential Difference = work done per unit charge
Let the total charge flows through the wire is "q" therefore

$P.D.=work/charge$

$P.D.=F.d/q$

$P.D.=e(B\times v)L/e$

$P.D.=L(B\times v)$

or

$P.D.=BvLsin\theta$

This is called motional EMF.
3 years ago
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