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Question
A conducting circular loop having a radius of 5.0 cm, is placed perpendicular to a magnetic field of 0.50 T. It is removed from the field in 0.50 s. Find the average emf produced in the loop during this time.
Solution
Given:-
Magnetic field intensity, B = 0.50 T
Radius of the loop, r = 5.0 cm = 5 × 10−2 m
∴ Area of the loop, A = πr2
Initial magnetic flux in the loop, ϕ1 = B × A
ϕ1 = 0.5 × π(5 × 10−2)2 = 125π × 10−5
As the loop is removed from the magnetic field, magnetic flux (ϕ2) = 0.
Induced emf ε is given by
\[\epsilon = \frac{\phi_1 - \phi_2}{t}\]
\[ = \frac{125\pi \times {10}^{- 5}}{5 \times {10}^{- 1}}\]
\[ = 25\pi \times {10}^{- 4}\]
= 25 × 3.14 × 10−4
= 78.5 × 10−4 V = 7.8 × 10−3 V
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