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

Solution

The magnetic field in between because of each of the conductors will be in naturally opposite directions.
∴ Net magnetic field
$straight B subscript in space between space space end subscript space equals space fraction numerator straight mu subscript straight o straight i over denominator 2 space straight pi space straight x end fraction space bold j with bold hat on top space plus space fraction numerator straight mu subscript straight o straight i over denominator 2 space straight pi space left parenthesis 2 straight d minus straight x right parenthesis end fraction left parenthesis negative straight j right parenthesis space equals space fraction numerator straight mu subscript straight o straight i over denominator 2 space straight pi space straight x end fraction space open square brackets 1 over straight x minus fraction numerator 1 over denominator 2 straight d minus straight x end fraction close square brackets space left parenthesis space bold j with bold hat on top space right parenthesis$
At x = d, B in between = 0
For x < d, B in between = $bold j with bold hat on top$
For x> d, B in between = $left parenthesis bold minus bold j with bold hat on top right parenthesis$
Towards x, net magnetic field will add up and direction will be $left parenthesis bold minus bold j with bold hat on top right parenthesis$ . Towards' x' b net magnetic field will add up and direction will be ( $bold j with bold hat on top$ )