Question

Two long parallel wires, AB and CD, carry equal currents in opposite directions. They lie in the xy plane, parallel to the x-axis, and pass through the points (0, -1, 0) and (0, 1, 0) respectively. The resultant magnetic field is :

• A. zero on the x-axis
• B. of all points on y-axis between the 2 wires , field is minimum on x-axis
• C. directed along the x-axis at the origin, but not at other points on the z-axis
• D. directed along the z-axis at all points on the x-axis

Answer 1

Answer: (B), (D)

The correct options are
B of all points on y-axis between the 2 wires , field is minimum on x-axis
D directed along the z-axis at all points on the x-axis

The magnetic field B at a distance r due to a long conductor carrying current I is
$B=\frac{{\mu }_{0}I}{2\pi r}$
Here, two long parallel wires, AB and CD, carry equal currents in opposite directions, hence the magnitude of the magnetic field at a distance a from the wires is
$B=2\frac{{\mu }_{0}I}{2\pi a}$
Hence it has minimum value at O.
Also the direction of current is opposite thus direction of magnetic field in between both conductors will be same and it is directed along Z-axis for all points on X-axis.