A conducting circular loop is placed in a uniform magnetic field of $0.02 T$ , with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of $1.0 m m / s$ , then find the emf induced in the loop, at the instant when the radius is $4 c m$ .

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Solution

induced EMF $E = - \frac{d ϕ}{d t}, ϕ = \to A . \to B, A = π R^{2}$
this gives , $E = - B \frac{d A}{d t} = - π B \times 2 R \frac{d R}{d t}$
$= π \times 0.02 \times 2 \times 0.04 \times 0.001$
$= 16 π \times 10^{- 7} V$

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A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.

induced EMF E=−dϕdt,ϕ=→A.→B,A=πR2this gives , E=−BdAdt=−πB×2RdRdt =π×0.02×2×0.04×0.001 =16π×10−7V

A conducting circular loop is placed in a uniform magnetic field of $0.02 T$ , with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of $1.0 m m / s$ , then find the emf induced in the loop, at the instant when the radius is $4 c m$ .

induced EMF $E = - \frac{d ϕ}{d t}, ϕ = \to A . \to B, A = π R^{2}$
this gives , $E = - B \frac{d A}{d t} = - π B \times 2 R \frac{d R}{d t}$
$= π \times 0.02 \times 2 \times 0.04 \times 0.001$
$= 16 π \times 10^{- 7} V$