SELECT * FROM question_mgmt as q WHERE id=635 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=3 AND subId=8 AND chapterId=120 and ex_no='1' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

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:

Length of the rectangular wire, l = 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 × 0.02

= 16 × 10−4 m2

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 × 10−4 V

Time taken to travel along the width , t = Distance traveled / Velocity = b / v

                                                                    =  0.02 / 0.01 = 2 s

Hence, the induced voltage is 2.4 × 10−4 V which lasts for 2 s.

(b) Emf developed, e = Bbv

= 0.3 × 0.02 × 0.01 = 0.6 × 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 × 10−4 V which lasts for 8 s.


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