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  4. Two very thin metallic wires placed along X and Y-axis carry equal currents as shown here. A B and C D are lines at 45° with the axes with origin of axes at O. The magnetic field will be zero on the line

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Q. Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $A B$ and $C D$ are lines at $45^{\circ}$ with the axes with origin of axes at $O$. The magnetic field will be zero on the linePhysics Question Image

Solution:

Every point on line $A B$ will be equidistant from $X$ and $Y$-axis. So magnetic field at every point on line $A B$ due to wire 1 along $X$-axis is equal in magnitude but opposite in direction to the magnetic field due to wire along $Y-$ axis. Hence $B_{\text {net }}$ on $A B=0$