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 0.3T 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?

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

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

Therefore, area of the rectangular loop, A = lb = 0.08 x 0.02 = 16×10<sup>-4</sup> m<sup>2</sup>

Magnetic field strength, B = 0.3 T

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<sup>-4</sup>V

Time taken to travel along the width, t = distance travelled/velocity = b/v = 0.02/0.02 = 2 s

Therefore, the induced voltage is 2.4×10<sup>-4</sup>V lasting for 2 s.

(b) EMF developed, e = Bbv = 0.3×0.02×0.01 = 0.6×10<sup>-4</sup>V

Time taken to travel along the length, t = distance travelled/velocity = l/v = 0.08/0.01 = 8 s

Therefore, the induced voltage is 0.6×10<sup>-4</sup>V lasting 8 s.

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