Question

A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.

Answer 1

Given: Length (l) = 50 cm = 0.5 m

Magnetic field (B) = 4.0 mT = 4 × 10⁻³ T

Angular speed 60 rpm = 1 rps

ω = 2π rad/s

Emf induced in a rotating rod about one end:

e = `1/2 B omega l^2`

= `1/2 xx 4 xx 10^-3 xx 2 pi xx (0.5)^2`

= 2 × 10⁻³ × 2π × 0.25

= π × 10⁻³

≈ 3.14 × 10⁻³ V

e ≈ 3.1 mV