Question

A conducting circular loop is placed in a uniform magnetic field B = 40 mT with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate 0.2 mm/s, then the induced emf in the loop at an instant when its radius is 1.0 cm is

• A. 0.1 πμV
• B. 0.2 πμV
• C. 1.0 πμV
• D. 0.16 πμV

Answer 1

Answer: (D)

0.16 πμV

Answer 2

$e = - B\frac{dA}{dt} = - B\frac{d}{dt}(\pi r^{2}) = - B\left( 2\pi r\frac{dr}{dt} \right) = 2\pi Br\left( - \frac{dr}{dt} \right)$

⇒$e = 2 \times \pi \times 40 \times 10^{- 3} \times 10^{- 2} \times (0.2 \times 10^{- 3}) = 0.16\pi\mu V$.