Question

An athlete with 3m long iron rod in hand runs towards east with a speed of 30 kmph. The horizontal component of earth's magnetic field is $4\times {10}^{-5}Wb/m^2$. If he runs with the rod in horizontal and vertical positions then the induced emf generated in the rod in two cases will be

• A. zero in vertical position and $1\times {10}^{-3}$ volt in horizontal position.
• B. $1\times 10$ volt in vertical position and zero volt in horizontal position.
• C. zero in both positions
• D. $1\times {10}^{-3}$ volt in both positions

Answer 1

The correct option is C zero in both positions

In both the cases, the velocity vector is $\overrightarrow{v}=30km/hr$ towards east
Magnetic field = $\overrightarrow{B}=4\times {10}^{-5}Wb/m^2$ towards north.

Force on a charge in the rod = $F=q\overrightarrow{v}\times \overrightarrow{B}=\frac{q}{3000}N$ towards vertically down direction.

Therefore, when the rod is horzontal no emf is induced between the two ends.
When the rod is vertical, emf = $Blv=1mV$ is induced between the two ends.