A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. [2023]

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Solution

Q.
A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be _________ $μ V$ . [2023]

Ans.
(50)

$\frac{d r}{d t} = 10^{- 3} m/s$

$\frac{d A}{d t} = 2 π r \frac{d r}{d t}$

$ε =$ $| \frac{- d ϕ}{d t} |$ $=$ $| \frac{B d A}{d t} |$

$= 0.4 \times 2 \times π \times 2 \times 10^{- 2} \times 10^{- 3} V$

$= 16 π μ V = 50.24 μ V$

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