A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 Ω is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (αt), where A = 80 μT and α = 50π rad/s. What is the magnitude of the current induced in the coil at t = 20 ms?
A) 11 mA
B) 18 mA
C) 14 mA
D) 22 mA
E) zero

Question

Quizplus · Accepted Answer

The magnitude of the induced emf is given by:ε = -dΦ/dt = -πr²NABcos(αt)where Φ is the magnetic flux through the coil, r is the radius of the coil, N is the number of turns, A is the amplitude of the magnetic field, and α is the angular frequency.The current induced in the coil is given by:I = ε/R = -πr²NABcos(αt)/RAt t = 20 ms, the magnitude of the current induced in the coil is:I = -π(0.15 m)²(50)(80 μT)cos(50π rad/s * 0.02 s)/4.0 Ω = 11 mA

A 50-Turn Circular Coil (Radius = 15 Cm) with a Total