A circular current loop of radius R carrying a current I is centered at the origin with its axis along the x axis. Its current is such that it produces a magnetic field in the positive x direction.

(a) Sketch a graph of Bx versus x for points on the x axis. Include both positive and negative values of x. Compare this graph with that for Ex due to a charged ring of the same size.

(b) A second, identical current loop, carrying an equal current in the same sense, is in a plane parallel to the yz plane with its center at x = d. Sketch graphs of the magnetic field on the x axis due to each loop separately and the resultant field due to the two loops. Show from your sketch that dBx /dx is zero midway between the two loops.