Question

Equal currents, of value 1A, are allowed to flow through a sequence of long wires, parallel to y–axis and located at, x = 1m, 2m, 4m and so on. If the currents flow in opposite directions in alternate wires, the value of magnetic field at the origin, O, is

(1) \(\frac{μ_0i}{3\pi}\) along z–axis

(2) \(\frac{3μ_0i}{4\pi}\) along x–axis

(3) \(\frac{i}{4\pi /μ_0}\) along z–axis

(4) \(\frac{μ_0i}{3\pi}\) along x–axis

Answer 1

(1) \(\frac{μ_0i}{3\pi}\) along z–axis

We know that the field at O, due to current i through one wire, is

Hence, for the whole sequence of wires, the desired field is