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 ___________. Numerical answer type. Work it out, then open the answer.

Answer: 50. e = B · 2π rdr/dt e = 0.4 × 2π × 0.02 × 10⁻³ = 1.6π × 10⁻⁵ V e ≈ 5.0 × 10⁻⁵ V So the induced emf is about 50 μ V.

A conducting circular loop is placed in a uniform magnetic field of… | JEE Main 2023 (12 Apr, Shift 1)

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Magnetic Flux & Faraday's Law

A conducting circular loop is placed in a uniform magnetic field of $0.4\text{ T}$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $1\text{ mm/s}$ . The magnitude of induced emf in the loop at an instant when the radius of the loop is $2\text{ cm}$ will be ___________ $\mu\text{V}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 50

$e = B \cdot 2\pi r\frac{dr}{dt}$
$e = 0.4 \times 2\pi \times 0.02 \times 10^{-3} = 1.6\pi \times 10^{-5}$ V
$e \approx 5.0 \times 10^{-5}$ V
So the induced emf is about $50\ \mu$ V.

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