A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field?
A) 59 mT
B) 62 mT
C) 65 mT
D) 68 mT
E) 31 mT

Question

Quizplus · Accepted Answer

The maximum value of the induced emf (ε_max) in a coil can be calculated using Faraday's law of electromagnetic induction, which states that ε_max = NABωsin(ωt), where N is the number of turns, A is the area of the coil, B is the maximum magnetic field, and ω is the angular frequency. Given that ε_max = 4.2 V, N = 400 turns, radius r = 1.0 cm = 0.01 m (thus, A = πr^2 = π(0.01)^2 m^2), and frequency f = 90 Hz (thus, ω = 2πf = 2π(90) rad/s), we can solve for B.First, calculate the area A = π(0.01)^2 = 3.14 × 10^-4 m^2. Then, ω = 2π(90) = 180π rad/s. Plugging these values into the equation for ε_max and solving for B gives:4.2 V = (400)(3.14 × 10^-4 m^2)(B)(180π rad/s)Solving for B yields approximately 0.059 T or 59 mT.

A 400-Turn Circular Coil (Radius = 1