Question

Two wires of large length carry equal currents each i. One wire is kept along x-axis and the other is kept along y-axis. the magnitude of magnetic field at a point on z-axis at distance d from the origin is

• A. $\frac{{\mu }_{0}i}{2\pi d}$
• B. $\frac{{\mu }_{0}i}{\sqrt{2}\pi d}$
• C. $\frac{{\mu }_{0}i}{\pi d}$
• D. Zero

Answer 1

Answer: (B)

$\frac{{\mu }_{0}i}{\sqrt{2}\pi d}$

$B=By+Bx$
$=\left(\frac{{\mu }_0}{2\pi }\right)\frac{I}{d}\hat{i}+\left(\frac{{\mu }_0}{2\pi }\right)\frac{I}{d}\hat{j}$
$=\left(\frac{{\mu }_0}{2\pi }\right)\frac{I}{d}\sqrt{2}=\frac{{\mu }_{0}i}{\sqrt{2}\pi d}$