Time-Variable Magnetic Flux

Twelve turns of wire of total resistance 8 ohms have a diameter of 7 cm and are oriented in the y-z plane. A variable magnetic field is directed along the x-axis:

If the turns are connected to an ammeter, what current will be read at t = 3 sec?

Solution:

The equations we need to use are:

Because the magnetic field is independent of the area, it can be taken outside of the integral:

At t = 3 sec, this rate of change of the flux has a value of 4.46 mV. Substituting it into Ohm's Law,

Because there are 12 turns, the current is (12)(0.558 mA) = 6.69 mA