Figure shows a straight, long wire carrying a current i and a rod of length ℓ coplanar with the wire and perpendicular to it. The rod moves with a constant velocity v in a direction parallel to the wire. The distance of the wire from the centre of the rod is x. Find the motional emf induced in the rod.
Given:
Current = i
Length of rod = l
Velocity = v
Distance of centre of rod from wire = x
Hence, the two ends of the rod are at distances 
and 
from the wire
Diagram:
Formula used:
We consider an element of length da at a distance of ‘a’ from the wire.
Now, magnetic field due to an infinite current carrying wire at a distance a
… (i), where μ0 = magnetic permeability of vacuum, i = current, a = distance from wire.
Therefore, emf induced in the element 
… (ii), where B = magnetic field, da = element, v = velocity
Hence, putting (i) in (ii), we get
Integrating on both sides and putting suitable limits, we get
⇒ 
(ans)