A conducting circular loop is placed in a uniform magnetic field of 0.5 T, with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at the rate of 4 mm/s. When the radius of the loop is 4 cm, the induced emf in the loop is

$160π\, μV$

The correct answer is Option (42) → $160π\, μV$

Induced emf = rate of change of magnetic flux

Magnetic flux = B × Area
Area of circle = πr²

emf = B × d(Area)/dt = B × 2πr × (dr/dt)

• B = 0.5 T
• r = 4 cm = 0.04 m
• dr/dt = 4 mm/s = 0.004 m/s

emf = 0.5 × 2π × 0.04 × 0.004
= 0.5 × 2π × 0.00016
= 0.5 × 0.00032π
= 0.00016π V

= 0.00016π× 10⁶μV
= 160π μV