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'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

Answer:

length of rectangular loop, l = 8cm = 0.08m

width of rectangular loop , b = 2cm = 0.02m

area of loop, A = l × b = 0.08 × 0.02 = 1.6 × 10^-3 m²

magnetic field strength, B = 0.3T

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

(a) emf developed in the loop is given as

e = Blv

= 0.3 × 0.08 × 0.01 = 2.4 × 10^-4V

time taken to travel along the width,t = distance travelled/velocity = b/v

= 0.02/0.01 = 2 s

hence, the induced voltage is 2.4 × 10^-4V which lasts for 2s

(b) emf developed , e = Bbv

= 0.3 × 0.02 × 0.01 = 0.6 × 10^-4V

time taken to travel along length , t' = l/v

= 0.08/0.01 = 8s

hence,the induced voltage is 0.6 × 10^-4V which lasts for 8s