Question

The coil shown in the figure has a resistance of 3.0 ?, 2 turns, a cross-sectional area of 0.20 m^2, and a field (parallel to the axis of the coil) with a magnitude given by B(t) = (4.0 + 3.0t^?2) T, where t is in s. What is the value of the induced current in the wire at t=3.5 s? Does this current flow from point A to point B or from point B to point A through the resistor? Answer is 2.8 A, Please fully explain.

Answer 1

magnetic flux through the coil is given as

$\phi$ = NBA

induced emf is given as

E = - d $\phi$ /dt = -NA (dB/dt)

E = NA (dB/dt)

E = (NA) (6t)

at t = 3.5 sec

E = (2) (0.2) (6) (3.5)

E = 8.4 volts

induced current is given as

i = E/R = 8.4 / 3 = 2.8 A