A straight thick long wire of uniform cross-section of radius a is carrying a steady current I. Calculate the ratio of magnetic field at a point `a//2` above the surface of the wire to that at a point `a//2` below its surface. What is the maximum value of the field of this wire?

Explanation

To solve the problem, we need to calculate the magnetic field at two points: one above the surface of the wire and one below the surface of the wire. We will then find the ratio of these two magnetic fields and determine the maximum magnetic field produced by the wire.

### Step-by-Step Solution:

1. **Identify the Points**:
- Let the radius of the wire be \( a \).
- The point above the surface of the wire is at a distance \( \frac{a}{2} \) from the surface, which means it is at a distance \( \frac{3a}{2} \) from the center of the wire.
- The point below the surface of the wire is at a distance \( \frac{a}{2} \) from the surface, which means it is at a distance \( \frac{a}{2} \) from the center of the wire.
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