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.

Explanation:

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