If there is a coil of wire with radius r = 15.4 cm with resistance per unit length λ = 0.331 Ω/m in magnetic field with changing induction B = B0 * cos(ωt), where B0 = 0.35T and ω = 4.1 rad/s and coil is rotating around its diameter with speed ω (at t = 0 the coil is perpendicular to the magnetic field) what is the average thermal power emitted by this coil?
I tried to solve this problem by calculating the amplitude of the emf with equations V = ΔΦ/Δt, Φ = Bπ(r^2)sin(ωt), the amplitude would be B0 * π(r^2). Then calculating the rms value, Vrms = V/√2 and squaring it and dividing it by R = 2πrλ (from P = V^2/R). I calculated P = 0.001061 W, but the site I got this problem from is telling me it's the wrong answer. I'm not sure if talking about emf in closed loop of wire is correct, but I don't know how to deal with this problem otherwise. If someone can tell me what did I do wrong, that would be great. (Sorry for potential language mistakes).