Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A long hollow pipe has an inner radius of mm and an outer radius of mm. It carries A, spread evenly over the metal of its wall. Find the field at mm from the axis, at mm from the axis, and at mm from the axis.
Ampere's law: , where only the net current through the loop counts. A round path of radius round a long wire gives . In a wire of radius with an even current, for .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. A, inner radius mm, outer radius mm.
Step 1. At mm. The circle is in the hollow part. No current goes through it, so .
Step 2. At mm, in the wall. The metal inside the circle has an area in proportion to (in mm divided by ). The whole wall has . So A. Then , that is .
Step 3. At mm, outside. All the current goes through the circle. , that is .
Answer: , , and .
Check. The field must grow from at the inner surface to its largest value at the outer surface, then fall. At mm it is . The values , , and then follow this rule.
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