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?

Length of the rectangular wire, 1 = 8 cm = 0.08 m

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

Hence, area of the rectangular loop, A = lb = 0.08 x 0.02 = 16 x 10⁻⁴ m²

Magnetic field strength, B = 0.3 T

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

Ans (a).

Emf developed in the loop is given as :

e =Blv = 0.3 x 0.08 x 0.01

= 2.4 x 10⁻⁴ V

Time taken to travel along the width ,

l = Distance travelled /(Velocity) = b/v= 0.02 /0.01 = 2 s

Hence, the induced voltage is 2.4 x 10^-4 V which lasts for 2 s.

Ans (b).

Emf developed, e = Bbv = 0.3 x 0.02 x 0.01 = 0.6 x 10⁻⁴ V

Time taken to travel along the length, t =Distance traveled /Velocity =l/v

=0.08/0.01 = 8 s

Hence, the induced voltage is 0.6 x 10^-4 V which lasts for 8 s.

(a] Emf developed in the loop is given as:

e=Blv = 0.3×0.08×0.01

= 2.4 x 10^-4 V