(a) Using Gauss's law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density `sigma C//m^(2)`. Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative.
(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 `mu C//m^(2)`. Calculate the
(i) charge on the sphere
(ii) total electric flux passing through the sphere.

Explanation

### Step-by-Step Solution

#### Part (a): Electric Field Intensity Outside a Uniformly Charged Thin Spherical Shell

1. **Understanding the Setup**:
- We have a uniformly charged thin spherical shell of radius \( R \) with a surface charge density \( \sigma \) (C/m²).
- We want to find the electric field intensity \( E \) at a point outside the shell, at a distance \( r \) from the center of the shell where \( r > R \).

...