Two long parallel wires are at a distance ` 2d` apart. They carry steady equal currents flowing out of the plane of the paper , as shown. The variation of the magnetic field `B` along the line `XX` is given by

Options

A.
B.
C.
D.

Answer

B

Explanation

Magnetic field induction due to a straight long conductor at a distance r away from it is given by
`B=(mu_0)/(4pi)(2I)/(r)`. Its direction is given by Right hand thumb rule. The magnetic field induction due to current in the two wires in the space between them is in opposite direction, therefore, the net magnetic field is
`B=(mu_0)/(4pi)(2I)/(x)hatj-(mu_0)/(4pi)(2I)/((d-x))hatj`
At mid point, `x=d//2`, the magnetic field B is zero.
At `xlt d//2`, the magnetic field B is along `hatj`. At `xgtd//2` the magnetic field is along `-hatj`. When x is negative, then the value of B is negative. When `xgtd`, then the value of B is positive. Therefore, the correct option is as shown in figure.