Question

A rectangular loop of sides l and b and resistance ‘R’ is kept in a region in which the magnetic field varies as B = B₀ sin ωt.

1. Derive expression for the emf induced in the loop.
2. Find the effective value of current that flows in the loop.

Answer 1

i. Expression for Induced emf:

Area of the loop (A) = l × b

Magnetic Flux (Φ) = B × A 

= (B₀ sin ωt) · (lb)

According to Faraday’s law:

ε = `-(d Phi)/dt`

= `-d/dt(l b B_0 sin omega t)`

= −lbB₀ω cos ωt

ii. Effective value of Current:

Instantaneous current (i) = `epsilon/R`

= `-(I b B_0 omega)/R cos omega t`

The peak value of current is (I₀) = `(I b B_0 omega)/R`

The effective (RMS) value of the current is:

I_eff = `I_0/sqrt 2`

= `(l b B_0 omega)/(sqrt 2 R)`