A round flat conducting loop is placed perpendicular to a uniform $0.50 \mathrm {~T}$ magnetic field. If the area of the loop increases at a rate of $3.0 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 } / \mathrm { s }$, what is the induced emf in the loop?
A) $4.3 \mathrm { mV }$
B) $0 \mathrm { mV }$
C) $5.5 \mathrm { mV }$
D) $1.7 \mathrm { mV }$
E) $1.5 \mathrm { mV }$

Question

Quizplus · Accepted Answer

The induced emf is given by Faraday's law of electromagnetic induction: $ \text{emf} = -\frac{d\Phi}{dt} $, where $ \Phi = B \cdot A $ is the magnetic flux. Since the magnetic field $ B = 0.50 \, \text{T} $ is constant and perpendicular to the loop, $ \frac{d\Phi}{dt} = B \cdot \frac{dA}{dt} = 0.50 \, \text{T} \times 3.0 \times 10^{-3} \, \text{m}^2/\text{s} = 1.5 \times 10^{-3} \, \text{V} = 1.5 \, \text{mV} $.

A Round Flat Conducting Loop Is Placed Perpendicular to a Uniform