Question

All straight wires are very long. Both $AB$ and $CD$ are arcs of the same circle, both subtending right angles at the centre $O$. Then the magnetic field at $O$ is-

• A. $\frac{{\mu }_{0}i}{4\pi R}$
• B. $\frac{{\mu }_{0}i}{4\pi R}\sqrt{2}$
• C. $\frac{{\mu }_{0}i}{2\pi R}$
• D. $\frac{{\mu }_{0}i}{2\pi R}(\pi +1)$

Answer 1

The correct option is C $\frac{{\mu }_{0}i}{2\pi R}$

$\begin{array}{c}B=\frac{{\mu }_{0}i}{4\pi R}+\frac{{\mu }_{0}i}{4\pi R}+\frac{{\mu }_{0}i\left(\frac{\pi }{2}\right)}{4\pi R}-\frac{{\mu }_{0}i\left(\frac{\pi }{2}\right)}{4\pi R}\\ =\frac{{\mu }_{0}i}{2\pi R}\end{array}$

Hence,

option $\left(C\right)$ is correct answer.