Question

Find the magnetic field of an infinitely long-current carrying wire with current I = A cos(wt) in the +x direction with w > 0 but small and constant and A > 0 constant.

Answer 1

I = A cos(wt) is the current flowing in infinitely long wire. We will assume that it is a staright wire.

Magnetic field due to this current in at a distance x from this wire will be given by:

B = (μ_o /2π ) * (I/x) ( It can be found using integration of magnetic field due tosmall current element in wire from - infinity to +infinity; using Biot-Savart law)

B = (μ_o /2πx ) * A cos (wt)

So, the magnitude of B will be varying with respect to time

NOTE: - Shape of infinitely long wire is very important. It is not mentioned in the question. I am assuming that it is staight).