Consider an infinetly long hollow cylindrical wire. The wire has an outer diameter b and the clindrical hole at its center has diameter a. Find the magnetic field everywhere if a known current i flows from left to right and the current is uniformly spread over the region between a and b.

B = (μ₀*i / (2*π*x)) * (x² - (a/2) ²) / ((b/2) ² - (a/2) ²)

Explanation:

Given

Outer diameter of the wire = b ⇒ R = b/2

Diameter of the clindrical hole at the center = a ⇒ r = a/2

The current that flows from left to right and is uniformly spread over the region between a and b = i

We apply Ampere's Law

Using the following formula for a/2 ≤ x ≤ b/2

B = (μ₀*i / (2*π*x)) * (x² - (a/2) ²) / ((b/2) ² - (a/2) ²)