Question

Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $AB$ and $CD$ are lines at $45^{\circ }$ with the axes with origin of axes at $O$. The magnetic field will be zero on the line

• A. AB
• B. CD
• C. Segment OB only of line AB
• D. Segment OC only of line CD

Answer 1

Answer: (A)

Every point on line $AB$ will be equidistant from $X$ and $Y$-axis. So magnetic field at every point on line $AB$ 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 $AB=0$