In Fig. 30-40a, a uniform magnetic field B increases in magnitude with time t as given by Fig. 30-40v, where the vertical axis scale is set by Bs = 12 mT and the horizontal scale is set by ts = 5.8 s. A circular conducting loop of area 9.6 10^-4 m^2 lies in the field, in the plane of the page. The amount of charge q passing point A on the loop is given in Fig. 30-40c as a function of t, with the vertical axis scale set by qs = 8.7 mC and the horizontal axis scale again set by ts = 5.8 s. What is the loop's resistance?
Explanation / Answer
Rate of change of magnetic field dB/dt = (Bs - 0) / (ts - 0) = (12 - 0) / (5.8 - 0) = 2.069 mT/s Current flowing in the loop I = dq/dt = (qs - 0) / (ts - 0) = (8.7 - 0) / (5.8 - 0) = 1.50 mA Induced EMF E = - d / dt = - A * dB / dt = - 9.6 * 10-4 * 2.069 * 10-3 = - 1.97 * 10-6 V Since - ve sign is indicative of direction only, hence it can be dropped. Resistance R = E / I = 1.97 * 10-6 / 1.5 * 10-3 = 1.31 * 10-3