Question

A square loop of side 10 cm, free to rotate about a vertical axis coinciding with its one arm, is initially held perpendicular to a uniform horizontal magnetic field of 0.2 T. If it is rotated at the uniform speed of 60 rpm, find the emf induced in the looр.

Answer 1

Given: Area (A) = (0.1 m)² = 0.01 m²

Magnetic field (B) = 0.2 T

f = 60 rpm = `60/60` rps = 1 Hz

Angular velocity (ω) = 2πf

= 2π(1)

= 2π rad/s

Induced EMF (ε) = BAω sin(ωt).

The peak value (ε₀) = NBAω

= 0.2 × 0.01 × 2π

= 0.002 × 2π

= 0.004 π V

ε₀ ≈ 0.01256 V

∴ The maximum induced emf is 0.004 π V (or approximately 1.26 × 10⁻² V).