Question

A one-meter-square coil of wire sits flat on a tabletop and bar magnet is dropped south-end-down toward it. As the magnet approaches, the field magnitude through the coil increases linearly from 4 mT to 16 mT is 0.25 s. This produces a 96 milliamp current circulating in the coil. Find the resistance of the coil, and state which way (as viewed from above) the induced current circulates.

An electric generator is intended to output 10 kJ of energy during each cycle. A 50-mT magnetic field will penetrate the circular coil, which is 0.5 m in radius and consists of 4000 turns of wire. The net average electrical resistance of the entire system is 10 ohms. Find the angular speed at which the coil (or magnetic field) must oscillate. Recall that Watt's Law gives the instantaneous power of any electrical element, and one cycle of time is two pi over the angular frequency.

Answer 1

Change in magnetic field dB = 16 mT - 4 mT = 12 mT = 12 x10 ^-3 T

Time interval dt = 0.25 s

Induced current i = 96 mA = 96 x10 ^-3 A

Area of square loop A = 1 m ²

Induced emf E = d(BA)/dt

                     = A dB / dt

                     = (1) (12 x10 ^-3 ) /(0.25)

                     = 48 x10 ^-3 volt

We know i = E / R

From this resistance R = E / i

                                  = (48 x10 ^-3 ) / (96x10 ^-3 )

                                  = 0.5 ohm