A sphere of radius R, uniformly charged with the surface charge density `sigma` rotates around the axis passing through its centre at an angular velocity. (a) Find the magnetic induction at the centre of the rotating sphere. (b) Also, find its magnetic moment.

Explanation

To solve the problem of finding the magnetic induction at the center of a rotating uniformly charged sphere and its magnetic moment, we can follow these steps:

### Step-by-Step Solution

**(a) Finding the Magnetic Induction at the Centre of the Rotating Sphere**

1. **Understanding the Charge Distribution**:
The sphere has a uniform surface charge density \( \sigma \). The total charge \( Q \) on the sphere can be calculated using the formula:
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