Two long parallel wires, AB and CD, carry equal currents in opposite directions. They lie in the x-y plane, parallel to the x-axis, and pass through the points (0,-a,0) and (0,a,0) respectively, Figure. The resultant magnetic field is:

Options

A. zero on the x-axis
B. maximum on the x-axis
C. directed along the z-axis at the origin, but not at other points on the z-axis
D. directed along the z-axis at all points on the z-axis.

Answer

B, D

Explanation

The magnetic field at a point on x-axis due to currents through AB and CD will be maximum, given by
`B=B_1+B_2=(mu_0)/(4pi)(2I)/(a)+(mu_0)/(4pi)(2I)/(a)=(mu_0I)/(a)`
acting along z-axis
The resultant magnetic field will be directed along the z-axis at all points on the z-axis.