A circular wire loop of radius 8.4 m lies in a plane perpendicular to a uniform magnetic field of magnitude 0.4 T. In 0.1 s the wire is reshaped into a square but remains in the same plane. What is the magnitude of the average induced emf in the wire during this time? Answer in units of V.

Given that,

Circular loop

Radius of loop

R = 8.4m

Area of a circle

A1 = πr² = π * 8.4² = 221.67m²

Magnetic field B = 0.4T

Time take t = 0.1sec

The wire is reshaped to square

Length of wire can be calculated using perimeter of a circle

P = 2πr

P = 2π * 8.4 = 52.78m

Which is the length of the square, therefore each side of the square is

L = 52.78/4 = 13.19m

Area of a square

A2 = L² = 13.19² = 174.1

EMF cam be calculated using.

EMF = - dΦ/dt

Where Φ = B•A•Sinθ

Since the field is perpendicular to the plane. then, θ=90° and Sinθ = 1

EMF = - dΦ/dt

EMF = - d (BA) / dt

B is constant

EMF = - B•dA/dt

EMF = - B ∆A/∆t

EMF = - B * (A2-A1) / (t2-t1)

EMF = - 0.4 * (174.01 - 221.67) / 0.1

EMF = - 0.4 * - 47.57 / 0.1

EMF = 190.28 Volts

The magnitude of induced EMF is 190.28 V