A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.500~\text{T}0.500 T so that the plane of the coil makes an angle of 30^\circ30 ∘ with the magnetic field. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in 0.100~\text{s}0.100 s.

3.9 V

Explanation:

Parameters given:

Number of turns, N = 50

Diameter of coil = 15 cm = 0.15 m

Radius of coil, r = 0.075 m

Magnetic field, B = 0.5 T

Angle = 30°

Time, t = 0.1 secs

E. M. F induced is given as:

EMF = (B * A * N * cos30) / t

Where A = area of coil = pi * r²

A = 3.142 * 0.075² = 0.018 m²

EMF = (0.5 * 0.018 * 50 * 0.866) / 0.1

EMF = 3.9 V

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