A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius alpha. (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surface?

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Finding Surface Charge Densities on Inner and Outer Surfaces

1. **Understanding the Setup**:
- We have a hollow metallic sphere of radius \( \alpha \) that is initially uncharged.
- A charge \( Q \) is placed at the center of the sphere.

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