Question

A conducting circular loop of area 1 mm² is placed coplanarly with a long, straight wire at a distance of 20 cm from it. The straight wire carries an electric current which changes from 10 A to zero in 0.1 s. Find the average emf induced in the loop in 0.1 s.

Answer 1

Given:-
Area of the loop, A = 1 mm²
Current through the wire, i = 10 A
Separation between the wire and the loop, d = 20 cm
Time, dt = 0.1 s
The average emf induced in the loop is given by

\[e = \frac{d\phi}{dt}\] 

\[       = \frac{BA}{dt} = \frac{\mu_0 i}{2\pi d} \times \frac{A}{dt}\] 

\[       = \frac{4\pi \times {10}^{- 7} \times 10}{2\pi \times 2 \times {10}^{- 1}} \times \frac{{10}^{- 6}}{1 \times {10}^{- 1}}\] 

\[       = 1 \times  {10}^{- 10}   V\]