Question

A conducting circular loop having a radius of 5.0 cm, is placed perpendicular to a magnetic field of 0.50 T. It is removed from the field in 0.50 s. Find the average emf produced in the loop during this time.

Answer 1

Given:
Magnetic field intensity, B = 0.50 T
Radius of the loop, r = 5.0 cm = 5 × 10⁻² m
∴ Area of the loop, A = $\mathrm{\pi }{r}^2$
Initial magnetic flux in the loop, ϕ₁ = B × A
ϕ₁ = 0.5 × $\mathrm{\pi }$(5 × 10⁻²)² = 125$\mathrm{\pi }$ × 10⁻⁵
As the loop is removed from the magnetic field, magnetic flux (ϕ₂) = 0.
Induced emf ε is given by
$$\begin{gathered} \mathrm{\epsilon }=\frac{{\mathrm{\varphi }}_1-{\mathrm{\varphi }}_2}{t} \\ =\frac{125\mathrm{\pi }\times {10}^{-5}}{5\times {10}^{-1}} \\ =25\mathrm{\pi }\times {10}^{-4} \end{gathered}$$
= 25 × 3.14 × 10⁻⁴
= 78.5 × 10⁻⁴ V = 7.8 × 10⁻³ V