Question

A copper rod moves parallel to the horizontal direction. The induced emf developed across its ends due to earth's magnetic field will be maximum at the

• A. equator
• B. latitude ${30}^o$
• C. latitude ${60}^o$
• D. poles

Answer 1

The correct option is D

poles

Explanation for the correct option:

1. Earth acts like a magnetic dipole.
2. This means that the earth is like a bar magnet.
3. According to Lorentz's force, the magnetic field is more where there is more movement of charges.
4. The magnetic field lines density is maximum at the poles and minimum at the center of the line joining the two poles.
5. The relationship between magnetic field strength and emf induced is,
   $e=Blv\sin \theta$
   where $e$ is the induced emf, $B$ is the strength of the magnetic field, $l$ is the length of the coil, $v$ is the velocity of the coil and $\theta$ is the angle between velocity and magnetic field vector.
6. At the poles, the magnitude of the vertical component of the earth's magnetic field is maximum.
7. So here, with the rod moving parallel to the horizontal direction,
   $$\begin{gathered} \theta =\frac{\mathrm{\pi }}{2} \\ \Rightarrow \sin \theta =1 \\ \Rightarrow e=Blv \end{gathered}$$
8. Hence, emf induced is maximum at poles.

Hence, option D is correct.