Question

A rectangular coil with sides 0.130 m by 0.250 m has 513 turns of wire. It is rotated about its long axis in a uniform magnetic field of 0.550 T that is perpendicular to the long axis. At what frequency, in complete cycles per second, must the coil be rotated for it to generate a maximum voltage of 115 V?

Answer 1

Voltage = N * Δ(BA)/Δt 
BA = 0.57*0.16*0.22 = 2.0064e-2 
N = 505 
115/505 = Δ(BA)/Δt = 23/101 
When the top of the coil rotates to the bottom (1/2 half cycle) BA changes from max to min and when the bottom rotates back to the top BA changes from min to max. So Δ(BA) is twice per cycle 
So 2*101Δ(BA)=23Δt and Δt = 1/f 
202*2.0064e-2/23 =Δt = 1/f => f =5.675Hz