# Define motional emf and derive an expression for it.

Apoorva Arora IIT Roorkee
10 years ago
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.
Thanks and Regards
Apoorva Arora
IIT Roorkee
NIKHIL
15 Points
5 years ago
dfi=B.dA
=B.I.V.dt
=> €= -dfi/dt
Therefore, €= -BIV
This emf is called motional emf.
Direction of induced current by Fleming's Right Hand Rule.
Consider a  rod moving in a magnetic field with a velocity v. We know that the rod is containing some free electrons which drift in the rod  towards an end due to magnetic force leading to charge seperated in the rod. Now we can see q(v×B)=qE hence we obtain expression for the induced electric field E = Bv now we now total emf developed in the rod  $\int_{0}^{L}(E.dx) = BvL$