Question

A cylindrical cable of radius 8.57 mm carries a current of 25.5 a, uniformly spread over its cross-sectional area. at what distance from the center of the wire is there a point within the wire where the magnetic field is 0.447 mt?

Answer 1

I think there is a problem with this question because the answer is not inside the wire as stated, but would require a bigger wire than stated. This should be a standard ampere's law problem, B = I(mu), where B is the magnetic field, I is the current and mu is the magnetic permitivity constant (4*pi * 10^-7 H/m or T/A). We can describe the amount of current we get from our distance from the center of the wire with a ratio of areas (pi*r^2/pi*d^2), where r is our particular distance from the center (what we're trying to find) and d is the total radius of the wire. Adding this into ampere's law and canceling the pi's we get B = I*(mu)*(r^2/d^2), solving for r we get r = sqrt(B*d^2/(I*(mu))), when you plug values in, it gives an r of 32mm, which is much bigger than the actual radius of the wire. Maybe something was copied wrong?