Two long parallel wires are at a distance 2d | vedclass

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(B) Let the two wires be at positions $x = -d$ and $x = +d$ on the $XX'$ axis. Both carry current $I$ in the outward direction (perpendicular to the p

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(B) Let the two wires be at positions $x = -d$ and $x = +d$ on the $XX'$ axis. Both carry current $I$ in the outward direction (perpendicular to the plane of the paper).The magnetic field due to a single wire at a distance $r$ is $B = \frac{\mu_0 I}{2\pi r}$.Using the right-hand rule,for a wire carrying current out of the plane,the magnetic field lines are counter-clockwise.For the wire at $x = -d$,the field is $B_1 = \frac{\mu_0 I}{2\pi (x+d)}$ (directed upwards for $x > -d$).For the wire at $x = +d$,the field is $B_2 = \frac{\mu_0 I}{2\pi (x-d)}$ (directed upwards for $x > d$,but downwards for $x At the midpoint $(x=0)$,the fields are equal and opposite,so the net field is $0$.To the left of $x = -d$,both fields point downwards. To the right of $x = +d$,both fields point upwards.Between the wires,the fields oppose each other,resulting in a curve that passes through zero at the center and changes sign. The correct graphical representation is Option $B$.

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

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