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bitty
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Homework Statement
Two infinitely long identical conductors carry equal current densities J in opposite directions parallel to the z-axis. They each have radius b and overlap so their centers are distance 2a apart. In the overlap a distance a from the center we have 0 current density (a hollow region).
What is the direction and magnitude of the magnetic field at the center of the hollow region?
Along the y-axis at x=0? All throughout the region?
Homework Equations
ampere's law
The Attempt at a Solution
I concluded the magnetic field everywhere inside the hollow region is the same:
B*2*pi*r=4*pi/c*J*pi*r^2 in cgs units for each cylinder
so B = 2*pi/c*J*(r2-r1)
where r2-r1 is a constant, r2 the distance from one cylinder to any pt inside the region and r1 equivalently for the other cylinder. since r2-r1 is vector addition it equals 2a, the distance between the centers of the cylinders, so B is constant for all 3. By the right hand rule, B points straight up in +y direction.
Could someone please check?