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.

\[\therefore e=1 \times 0 . 2 \times 0 . 1 \times \sqrt{\frac{3}{2}}\]

= 17.32 × 10⁻³ V