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 = πr²

Initial magnetic flux in the loop, ϕ₁ = B × A
ϕ₁ = 0.5 × π(5 × 10⁻²)² = 125π × 10⁻⁵
As the loop is removed from the magnetic field, magnetic flux (ϕ₂) = 0.
Induced emf ε is given by

\[\epsilon = \frac{\phi_1 - \phi_2}{t}\]

\[ = \frac{125\pi \times {10}^{- 5}}{5 \times {10}^{- 1}}\]

\[ = 25\pi \times {10}^{- 4}\]

= 25 × 3.14 × 10⁻⁴

= 78.5 × 10⁻⁴ V = 7.8 × 10⁻³ V