Question

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 × 10^-5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in µV) in the coil will be close to the integer ______.

विकल्प

• 10

• 15

• 20

• 25

Answer 1

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 × 10^-5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in µV) in the coil will be close to the integer 15.

Explanation:

Given: The radius of the circular coil is R = 10 cm, the magnitude of the uniform magnetic field in the region is B = 3.0 10^-5 T, and the initial angle between the plane of the coil and `vec"B"` is = `pi/2`. The coil rotates perpendicular to `vec"B"` and completes half a rotation in t = 0.2 s.

To find: ε₀, maximum value of induced e.m.f. in the coil.

Let A be the area of the coil and ω be its angular speed.

Flux through the coil:

Φ = BA cos ωt

E.m.f. induced in the coil:

ε = `("d"phi)/"dt"` = BAωsin ωt

Maximum e.m.f induced in the coil:

ε₀ = BAω

ε₀ = B(πr²) `(pi/0.2)`

= 15 μV.