Question

Two very thin metallic wires placed along X and Y axes carry equal currents as shown in the figure. AB and CD are lines at ${45}^0$ with the axes having origin at O, then the magnetic field will be zero on the line

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

Answer 1

The correct option is A AB

AB is the line on which the magnetic field of both the wires will cancel out. On CD, it will be added.

field due to X wire at $P=\frac{{\mu }_o}{2\pi }\frac{2i}{d}$ outside of page

field due to Y at $P=\frac{{\mu }_o}{2\pi }\frac{2i}{d}$ inside of page

find direction using right hand thumb rule

$\therefore$ at any point P on line AB,

$Field=\frac{{\mu }_{o}2i}{2\pi d}-\frac{{\mu }_{o}2i}{2\pi d}$

$=$zero