A conducting loop of area 5.0 cm ^2 is placed in a magnetic field which varies sinusoidally with time as B = B₀ t where B₀ = 0.20 T and = 300 s ⁻¹ . The normal to the coil makes an angle of 60^ with the field. Determine the maximum emf induced in the coil.

Step-by-step solution

The magnetic flux linked with the loop is given by = B A = B A . Substituting the given values, = (B₀ t) A 60^ . The induced emf is = - d dt = -B₀ A 60^ t . The maximum induced emf is _ max = B₀ A 60^ . Given B₀ = 0.20 T , A = 5.0 10⁻⁴ m ^2 , = 300 s ⁻¹ , and = 60^ . _ max = 0.20 5.0 10⁻⁴ 300 1 2 _ max = 1.0 10⁻⁴ 150 = 0.015 V .