Question

16)A triangular conducting loop lies in a uniform magnetic field B which varies with time as shown in 10 the graph. At t = 1 s the magnetic field is pointing out of the page. The triangle's height is-3 ma ptsFor what time interval(s) is the induced current in the loop equal to zero? (b) During what time interval (s) is the magnitude of the induced current a maximum? (c) What is the magnitude of the induced voltage at t = 2.5 s? (d) What is the direction of the induced current at t= 2.5 s? B(Tesla) 13m t(s) 2

Answer 1

(a) Chang in flux is given d phi/dt = d/dt (BA) = dB/dt + B middot dA/dt As are of loop is constant So dA/dt = 0 So d phi/dt = A dB/dt As E = IR = -d phi/dt So I = -1/R d phi/dt I = -A/R middot dB/dt \r\n As B is constant in the interval t = 1 or t = 2 So the d phi/dt = 0 for t = 1 so t = 2 So Induced current I = 0 for t = 1 to t = 2 (b) when change in magnetic field is maximum with time then induction of current will be maximum From t = 3 to t = 4 Magnetic field sharply goes to zero. Hence dB/dt is maximum for t = 1 to t = 4 So, I = -A/R middot dB/dt is maximum for t = 1 to t = 4 s (c) At t = 2.5 dB/dt = Delta B/Delta t = 2 - 1/3 - 2