A conducting circular loop with an area of 1 mm ^2 is positioned coplanarly with a long, straight wire at a distance of 20 cm from it. The electric current carried by the straight wire decreases from 10 A to zero in 0.1 s . Determine the average emf induced in the loop during this 0.1 s interval.

Step-by-step solution

Area of the loop, A = 1 mm ^2 = 10⁻⁶ m ^2 Distance from the wire, r = 20 cm = 0.2 m Initial current, I₁ = 10 A Final current, I₂ = 0 A Time interval, t = 0.1 s Since the loop is very small, the magnetic field can be considered uniform over its area. Magnetic field at distance r due to the straight wire is B = ₀ I 2 r Initial magnetic flux through the loop is ₁ = B A = ₀ I₁ A 2 r Final magnetic flux through the loop is ₂ = 0 Average induced emf is e = t = ₁ - ₂ t e = ₀ I₁ A 2 r t e = 4 10⁻⁷ 10 10⁻⁶ 2 0.2 0.1 e = 2 1