Question

A metallic wire bent in form of a semi-circle of radius 0.1 m is moved in a direction parallel to its plane, but perpendicular to a magnetic field $B=20$ mT with a velocity of 10 m/s. What is the induced e.m.f. in wire?

• A. $4\times {10}^{-3}$ volts
• B. $4\times {10}^{-2}$ volts
• C. $4\times {10}^{-1}$ volts
• D. None of these

Answer 1

Answer: (B)

$4\times {10}^{-2}$ volts

Consider an infinitesimally small element of length $Rd\theta$ in the wire.

Net emf developed across the element=$Bvsin\theta \left(Rd\theta \right)$

Thus the total emf in the wire across two ends=${\int }_0^{\pi }vsin\theta BRd\theta$

$=2BvR$

$=2\times 0.02\times 10\times 0.1volts$
$=0.04volts$