Question

A metallic rod of 1 m length is rotated with a frequency of 40 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field of 0.5 T parallel to the axis is present in the region. The value of emf induced between the centre and the metallic ring is close to:

विकल्प

• 20 V

• 32 V

• 40 V

• 63 V

Answer 1

63 V

Explanation:

Given: B = 0.5 T

L = 1 m

f = 40 rev/s

Formula: ω = 2πf

= 2π × 40

= 80π

For a rod rotating about one end in a uniform magnetic field (perpendicular to plane), induced emf

ε = `1/2 BωL^2`

= `1/2 xx 0.5 xx 80π xx (1)^2`

= 0.5 × 0.5 × 80π × 1

= 0.25 × 80π

= 20π

= 20 × 3.14

= 62.8

= 63 V