Physics question below?

Question

A very long, straight wire carries a current of 0.55 A. This wire is tangent to a single-turn, circular wire loop that also carries a current. The directions of the currents are such that the net magnetic field at the center of the loop is zero. Both wires are insulated and have diameters that can be neglected. How much current is there in the loop?

Answer 1

Since we are not given the diameter of the wire loop, let us say that the loop has a radius equal to R. Now, the magnetic field at a distance R from a very long wire with current I is B = (μo)I / (2πR), where μo is the magnetic permeability constant. The magnetic field at the center of a loop of wire with radius R is (μo)I / (2R). So to get a zero net magnetic field with unknown loop current x, we need (μo)(0.55 A) / (2πR) = (μo)x / (2R) ==> (0.55 A) / π = x ==> x = 0.175 A. As you can see, there is no dependence on the radius of the loop.