Question

A wire of length 10 cm translates in a direction making an angle of 60° with its length. The plane of motion is perpendicular to a uniform magnetic field of 1.0 T that exists in the space. Find the emf induced between the ends of the rod if the speed of translation is 20 cm s⁻¹.

Answer 1

Given:
Length of the rod, l = 10 cm = 0.1 m
Angle between the velocity and length of the rod, θ = 60°
Magnetic field, B = 1 T
Velocity of the rod, v = 20 cm/s = 0.2 m/s
The motional emf induced in the rod is given by
$e=\left(\overrightarrow{v}\times \overrightarrow{B}\right).\overrightarrow{l}$
∴ e = Bvl sin 60°
We take the component of the length vector that is perpendicular to the velocity vector.
∴ e = $1\times 0.2\times 0.1\times \sqrt{\frac{3}{2}}$
= 17.32 × 10⁻³ V