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?

Question

Duncan Fleming

Physics

28 September, 03:47

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?

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Aarav Stanton · 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