Figure a shows a wire that forms a rectangle W 150 cm H 30

Figure (a) shows a wire that forms a rectangle (W = 15.0 cm, H = 30.0 cm) and has a resistance of 5.00 m?. Its interior is split into three equal areas, with B1, B2, and B3. The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components Bz of the three fields with time t; the vertical axis scale is set by Bs = 3.50 ?T and Bb = -2.50Bs. What are the (a) the magnitude and (b) direction of the current induced in the wire?

Solution

We have a rectangle containing three areas with magnetic field lines coming out of it. Also, the magnetic field lines change in magnitude with time as depicted in the graph above.

As we need to determine the magnitude and direction of the current induced in the loop, we will need to determine the emf induced in the loop due to the changing magnetic flux. So as to determine the emf, we will find out the net flux through the loop at the end of the given time interval and the divide it by time to get the rate of change of magnetic flux which in turn is equal to the emf induced.

So, the net magnetic flux at the end of 2 seconds is:

= (B1 + B2 + B3) *15*10 * 10^-4

= (5.25 - 8.75) x 150 x 10^-4 x 10^-6= -525 x 10^-10 Tm^2

Therefore the emf induced = -525 x 10^-10 / 2 = -262.5 x 10^-10 Volts

a.) Magnitude of the current = 262.5 x 10^-10 / 5 x 10^-3 = 52.5 x10^-7 Amperes

b.) The direction of the current induced would be anti-clockwise.