A long straight wire of a curcular cross-section of radius 'a' carries a steady current 'l'. The current is uniformly distributed the across- section . Apply Amphere's circuital law to calculate the magnetic field at a point 'r' in the region for (i) `r lt a` and (ii) `r gt a`.

Explanation

To solve the problem of finding the magnetic field at a distance \( r \) from a long straight wire of circular cross-section carrying a steady current \( I \), we will apply Ampère's circuital law. We will consider two cases: when \( r < a \) (inside the wire) and when \( r > a \) (outside the wire).

### Step-by-Step Solution:

#### Case 1: \( r < a \)

1. **Identify the Current Density \( J \)**:
The current is uniformly distributed across the cross-section of the wire. The current density \( J \) can be defined as:
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