Question

A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm $s^{-1}$ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

Answer 1

Length of the rectangular wire, $l=8cm=0.08m$

Width of the rectangular wire, $b=2cm=0.02m$

Hence, area of the rectangular loop,

$A=lb$

$=0.08\times 0.02$

$=16\times {10}^{-4}{m}^2$

Magnetic field strength, $B=0.3T$

Velocity of the loop, $v=1cm/s=0.01m/s$

(a)

Emf developed in the loop is given as:

$e=Blv$

$=0.3\times 0.08\times 0.01=2.4\times {10}^{-4}V$

Time taken to travel along the width, $t=\frac{Distancetravelled}{Velocity}=\frac{b}{v}$

$=\frac{0.02}{0.01}=2s$

Hence, the induced voltage is $2.4\times {10}^{-4}V$ which lasts for 2 s.

(b)

Emf developed, $e=Bbv$

$=0.3\times 0.02\times 0.01=0.6\times {10}^{-4}V$

Time taken to travel along the length, $t=\frac{Distancetraveled}{Velocity}=\frac{l}{v}$

$=\frac{0.08}{0.01}=8s$

Hence, the induced voltage is $0.6\times {10}^{-4}V$ which lasts for 8 s.