A uniform magnetic field exists in a circular region of radius R centred at O. The field is perpendicular to the plane of paper and is strength varies with time as `B=B_(0)t`. Find the induced electric field at a distance r from the centre for (i)`r lt R`, (ii) `r gt R`. Also, plot a graph between `|E|` and r for both the cases.

Explanation

To solve the problem, we need to find the induced electric field at a distance \( r \) from the center \( O \) of a circular region where a magnetic field \( B \) is varying with time as \( B = B_0 t \). We will analyze two cases: (i) when \( r < R \) and (ii) when \( r > R \).

### Step-by-Step Solution:

#### Case (i): \( r < R \)

1. **Identify the Magnetic Flux**:
The magnetic flux \( \Phi_B \) through a circular area of radius \( r \) is given by:
...