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**1. Homework Statement**

There is a wire of radius r with a current i flowing through it. There is also a hole of radius a in the wire a distance b from the centre of the wire. The question asks, can you show that the magnetic field inside the hole is uniform? (assume that if you impose a current in the opposite direction where the hole is, that current has the same current density as in the actual conductor.)

My question is: how is the field inside the hole uniform? If the magnetic field gets stronger as r increases (the distance from the centre of the wire to anywhere in the wire), then wouldn't the magnetic field be larger at the outside edge of the hole rather than the inside edge? At both edges of the hole, the imposed opposite current would cause the same magnitude of B, would it not?

**2. Homework Equations**

ampere's law

**3. The Attempt at a Solution**

I know how to calculate B for the middle of the hole (it's just the magnetic field o the wire without the hole) and on the outer edge of the hole (magnetic field of wire w/o hole minus magnet field of hole), but when I calculate B on the inside of the hole, I get something different B2(pi)(b-a) = (mu)i(pi)(b-a)^2/(pi)(R^2 - a^2) ;

B = (mu)i(b-a)/2(pi)(R^2 - a^2) , but when I calculate be for the middle or outside of the hole, I get: (mu)ib/2(pi)(R^2 - a^2)