A circular coil having an area of 3.14 × 10^-2 m² and 30 turns is rotated about its vertical diameter with an angular speed of 70 rad^-1 in a uniform horizontal magnetic field of magnitude 5 × 10^-2 T. If the coil forms a closed loop of resistance 15 Ω, what is the average power loss due to Joule heating?

Given: N = 30; A = 3.14 × 10^-2 m² ; Angular velocity (ω) = 70 rad^-1; B = 5 × 10^-2 T; R = 15 Ω
Emf (E) = NABω
E = 30 × 3.14 × 10^-2 × 5 × 10^-2 × 70
E = 3.297 V
Current (I) = E/R
I = 3.29715
I = 0.2198 A
Average power loss (P) = $\frac{I^{2}R}{2}$
P = 0.2198² × 152
P = 0.362 W
Therefore, the average power loss due to Joule heating is 0.362 W.