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

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(A) Let the two wires be at positions $A$ and $B$ on the $XX'$ axis,separated by a distance $2d$. The currents in both wires are equal and flow out of

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(A) Let the two wires be at positions $A$ and $B$ on the $XX'$ axis,separated by a distance $2d$. The currents in both wires are equal and flow out of the plane of the paper.Using the right-hand thumb rule,the magnetic field due to a wire carrying current out of the plane is directed counter-clockwise.$1$. At the midpoint $C$ between $A$ and $B$,the magnetic field due to wire $A$ is directed upwards,and the magnetic field due to wire $B$ is directed downwards. Since the distances and currents are equal,the net magnetic field at $C$ is zero.$2$. To the left of $A$ (e.g.,at point $F$),both wires produce magnetic fields directed downwards. Thus,the net field is negative.$3$. Between $A$ and $C$,the field due to $A$ (upward) is stronger than the field due to $B$ (downward),so the net field is positive.$4$. Between $C$ and $B$,the field due to $B$ (downward) is stronger than the field due to $A$ (upward),so the net field is negative.$5$. To the right of $B$,both wires produce magnetic fields directed upwards. Thus,the net field is positive.This variation corresponds to a graph that passes through zero at the midpoint $C$,is positive between $A$ and $C$,and negative between $C$ and $B$. The correct graph is represented by option $A$.

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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