Assume Earth's surface is a conductor with a uniform surface charge density `sigma`. It rotates about its axis with angular velocity `omega`. Suppose the magnetic field due to Sun at Earth at some instant is a uniform field B pointing along earth's axis. Then the emf developed between the pole and equator of earth due to this field is. (`R_e =`radius of earth)

Options

A. `1/2 B omegaR_(e)^(2)`
B. ` B omegaR_(e)^(2)`
C. `3/2 B omegaR_(e)^(2)`
D. zero

Explanation

To solve the problem, we need to calculate the electromotive force (emf) developed between the pole and the equator of the Earth, which is treated as a conductor with a uniform surface charge density, rotating with angular velocity \( \omega \) in the presence of a uniform magnetic field \( B \) pointing along the Earth's axis.

### Step-by-step Solution:

1. **Understanding the Setup**:
- The Earth is modeled as a conductor with a uniform surface charge density \( \sigma \).
- It rotates about its axis with angular velocity \( \omega \).
- A uniform magnetic field \( B \) from the Sun is present, pointing along the Earth's axis.
...