AP EAPCET 06-Jul-2022 Shift 2 Paper

Given, I=I0sin‌ωt
Magnetic field inside the solenoid, B=µ0NI
⇒‌‌B=µ0NI0sin‌ωt .....(i)
When side of square loop be l, then
‌4l=2πR
⇒l=‌

πR

2

Area of square loop, A=l2
=(‌

πR

2

)2=‌

π2R2

4

Magnetic flux linked with square loop,
φ=BA
=‌µ0NI0sin‌ωt×‌

π2R2

4

φ‌=‌

µ0π2R2NI0sin‌ωt

4

Induced emf in the square coil, e=‌

dφ

dt

‌=‌

d

dt

‌

µ0π2R2NI0sin‌ωt

4

‌=‌

µ0π2R2NI0ω‌cos‌ω‌t

4

‌=2.46µ0R2NI0ω‌cos‌ω‌t
(∵‌

π2

4

=246)
Which is closest to the value given in option (c).