Using Gauss' law deduce the expression for the electric field due to a uniformly charged sperical conducting shell of radius R at a point (i) outside and (ii) inside the shell.
Plot a graph showing variation of electric field as a function of `r gt R and r lt R`. (r being the distance from the centre of the shell)

Explanation

To deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius \( R \) at a point outside and inside the shell using Gauss's law, we will follow these steps:

### Step 1: Understanding the Setup
Consider a uniformly charged spherical conducting shell of radius \( R \) with total charge \( Q \). We need to find the electric field \( E \) at a point \( P \) which is at a distance \( r \) from the center of the shell.

### Step 2: Electric Field Outside the Shell (\( r > R \))
1. **Choose a Gaussian Surface**: For points outside the shell, we choose a spherical Gaussian surface of radius \( r \) where \( r > R \).
2. **Apply Gauss's Law**: According to Gauss's law, the electric flux \( \Phi_E \) through the Gaussian surface is given by:
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