A conducting circular loop is placed in a uniform magnetic field 0....

A conducting circular loop is placed in a uniform magnetic field $0. 04T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2mms^{- 1}$ . The induced emf in the loop, when the radius is $2$ cm, is

Options

A $4. 8\pi\mu V$
B $0. 8\pi\mu V$
C $1. 6\pi\mu V$
D $3. 2\pi\mu V$

Correct answer

D. $3. 2\pi\mu V$

Step-by-step solution

ϕ = \text{BA} \text{cos} \theta = \text{B} \left(\pi r^{2}\right) \text{cos} {0}^{∘} = \text{B} \pi r^{2}

<br /><br />\left|ε\right| = \dfrac{\text{d} ϕ}{\text{dt}} = \text{B} \pi \left(2 \text{r}\right) \dfrac{\text{dr}}{\text{dt}}

= \text{0.04} \times \pi \times \left(2 \times 2 \times 1 {0}^{- 2}\right) \times 2 \times 1 {0}^{- 3}

= \text{3.2} \pi \times 1 {0}^{- 6} \text{V} = \text{3.2} \pi \mu \text{V}

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