Question

A circular loop of wire of resistance - 0.500 and radius 8.10 cm is in a uniform magnetic field directed out of the page as in the figure below. A clockwise current of 120 mA is induced in the loop. (a) is the magnetic field increasing or decreasing in time? decreasing (b) Find the rate at which the field is changing with time.

Answer 1

Solution) R = 0.500 ohm

r = 8.10 cm = 8.10×10^(-2) m

I = 3.20 mA = 3.20×10^(-3) A

(a) it indicates increasing magnetic field

(b) dB/dt = ?

I = E/R

E = - d(phi)/dt

phi = B.A = B.(pi)(r^2)

E = (pi)(r^2)(dB/dt)

I = ((pi)(r^2)(dB/dt))/(R)

(dB/dt) = ((I)(R))/((pi)(r^2))

dB/dt = (3.20×10^(-3)×0.500)/((pi)(8.10×10^(-2))^2)

dB/dt = 0.0776 T/s

dB/dt = 77.6 mT/s