Q. Two infinite length wires carry currents $8A$ and $6A$ respectively and are placed along $X$ and $Y$-axis. Magnetic field at a point $P(0,0,d)m$ will be
A) $\frac{7\mu_{0}}{\pi l}$
B) $\frac{10\mu_{0}}{\pi l}$
C) $\frac{14\mu_{0}}{\pi l}$
D) $\frac{5\mu_{0}}{\pi l}$
Explanation
(d) Magnetic field at $P$ due to wire 1, $B_{1} = \frac{\mu_{0}}{4\pi}.\frac{2(8)}{d}$
and due to wire $2,\ B_{2} = \frac{\mu_{0}}{4\pi}.\frac{2(6)}{d}$
$\Rightarrow B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}} = \sqrt{\left( \frac{\mu_{0}}{4\pi}.\frac{16}{d} \right)^{2} + \left( \frac{\mu_{0}}{4\pi}.\frac{12}{d} \right)^{2}}$
$= \frac{\mu_{0}}{4\pi} \times \frac{2}{d} \times 10 = 5\mu_{0}/\pi d$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.