First, we need to find the rate at which the area of the loop is changing since the induced emf in the loop is related to the change of magnetic flux through the loop.
The magnetic flux
Φ through the loop is given by:
Φ=B⋅Awhere
B is the magnetic field
and
A is the area of the loop.
The area
A of a circular loop with radius
r is given by:
A=Ï€r2The rate of change of the area
A with respect to time
t is:
‌=π‌(r2)=π⋅2r⋅‌We are given:
‌‌=−2‌mm‌ s−1=−2×10−3m s−1‌r=4‌cm=0.04m Substituting these values in, we get:
‌‌=π⋅2r⋅‌‌‌=π⋅2⋅0.04⋅−2×10−3‌‌=π⋅2⋅0.04⋅−2⋅10−3‌‌=−1.6×10−4πm2 s−1 The induced
emf‌ε is given by Faraday's law of induction:
ε=−‌Since
Φ=B⋅A, we have:
ε=−B⋅‌ Substituting the values of
B and
‌, we get:
‌ε=−0.125T⋅−1.6×10−4πm2 s−1‌ε=0.125⋅1.6×10−4π‌ε=2×10−5πVSince the question asks for the answer in
µV (microvolts), we convert the emf:
ε=20πµVThus, the correct answer is:
Option B:
20πµV