Question

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.

Answer 1

Answer:

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)