COMEDK 2024 Shift 2 Paper

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⋅A
where
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=πr2
The rate of change of the area A with respect to time t is:
‌

dA

dt

=π‌

d

dt

(r2)=π⋅2r⋅‌

dr

dt

We are given:
‌‌

dr

dt

=−2‌mm‌ s−1=−2×10−3m s−1
‌r=4‌cm=0.04m
Substituting these values in, we get:
‌‌

dA

dt

=π⋅2r⋅‌

dr

dt

‌‌

dA

dt

=π⋅2⋅0.04⋅−2×10−3
‌‌

dA

dt

=π⋅2⋅0.04⋅−2⋅10−3
‌‌

dA

dt

=−1.6×10−4πm2 s−1
The induced emf‌ε is given by Faraday's law of induction:
ε=−‌

dΦ

dt

Since Φ=B⋅A, we have:
ε=−B⋅‌

dA

dt

Substituting the values of B and ‌

dA

dt

, we get:
‌ε=−0.125T⋅−1.6×10−4πm2 s−1
‌ε=0.125⋅1.6×10−4π
‌ε=2×10−5πV
Since the question asks for the answer in µV (microvolts), we convert the emf:
ε=20πµV
Thus, the correct answer is:
Option B: 20πµV