Q.
A pair of stationary and infinite long bent wires are placed in the $x - y$ plane. The wires carrying currents of 10 A each as a shown in figure. The segments $L\ and\ M$ are parallel to $x$-axis. The segments $P\ and\ Q$ are parallel to $y$-axis, such that $OS = OR = 0.02$ m. The magnetic field induction at the origin O is
A) $10^{- 3}\ $T
B) $4 \times 10^{- 3}$ T
C) $2\ \times 10^{- 4}$ T
D) $10^{- 4}$ T
Explanation
(c) Total magnetic field induction at $O$ is
$\overrightarrow{\mathbf{B}} = {\overrightarrow{\mathbf{B}}}_{LR} + {\overrightarrow{\mathbf{B}}}_{RP} + {\overrightarrow{\mathbf{B}}}_{MS} + {\overrightarrow{\mathbf{B}}}_{SQ}$
$= 0 + \frac{\mu_{0}}{2\pi}\frac{i}{r} + 0 + \frac{\mu_{0}}{2\pi}\frac{i}{r} = \frac{\mu_{0}}{2\pi}\frac{2i}{r}$
$= \ \frac{2 \times 10^{- 7} \times 2 \times 10}{0.02} = 2 \times 10^{- 4}$ T
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.