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NCERT Class XII Chapter
Electromagnetic Induction
Questions With Solutions

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Question : 4
Total: 17
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 e.m.f developed across the cut if velocity of 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?
Solution:  

Here A = 8 × 2 = 16 cm2 = 16 × 10–4m2
B = 0.3 T
v = 1 cm s−1 = 10−2 m s−1
Induced emf, ε = ?
(i) When velocity is normal to longer side,
l = 8 cm = 8 × 10–2 m
ε = Blv = 0.3 × 8 × 10–2 × 10–2 = 2.4 × 10–4 V
Time , t =
distance‌moved
velocity
 =
2×10−2
10−2
 = 2 sec
(ii) When velocity is normal to shorter side,
l = 2 cm = 2 × 10–2 m
ε = Blv = 0.3 × 2 × 10–2 × 10–2 = 0.6 × 10–4 V
Time , t =
distance‌moved
velocity
 =
8×10−2
10−2
 = 8 sec
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