A conducting loop of area 5.0 cm^2 is placed in a magnetic field which varies sinusoidally with time as B = B base0 sin ωt where B base0 = 0.20 T and ω = 300 s^-1. The normal to the coil makes an angle of 60 with the field. Find (a) the maximum emf induced in the coil, (b) the emf induced at τ = (π/900)s and (c) the emf induced at t = (π/600) s.

Sol. A = 5 cm^2 = 5 x 10^–4 m^2 B = B0 sin ωt = 0.2 sin(300 t) θ = 60° a) Max emf induced in the coil E = dϕ/dt = d/dt (BA cosθ) = d/dt (B base 0 sin ω t x 5 x 10^-4 x 1/2) = B base 0 x 5/2 x 10^-4 d/dt (sin ωt) = B base 0 5/2 x 10^-4 cosωt . ω = 0.2x5/2 x 300 x 10^-4 x cos ωt = 15 x 10^-3 cos ωt E base max = 15 x 10^-3 = 0.015 V b) Induced emf at t = (π/900) s E = 15 x 10^–3 x cos ωt = 15 x 10^–3 x cos (300 x π/900) = 15 x 10^–3 x ½ = 0.015/2 = 0.0075 = 7.5 x 10^–3 V c) Induced emf at t = π/600 s E = 15 x 10^–3 x cos (300 x π/600) = 15 x 10^–3 x 0 = 0 V.