Question

In the given figure, what is the magnetic field induction at point O?

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

Answer 1

Answer: (C)

$\frac{{\mu }_{0}i}{4R}$ + $\frac{{\mu }_{0}i}{4\pi R}$

Length of $CD$ is very long.

Current flowing is $I$.

Here magnetic field $\left(B\right)$ at 0 is due to $ABC$ and $CD$ section.

$B$=field due to half circular section +long wire $C$ to $D$ outward from the plane of paper.

$B=|\frac{{\mu }_{0}I}{4R}+\frac{{\mu }_{0}I}{4\pi R}(\sin 90-\sin 0)|$

$=\frac{{\mu }_{0}I}{4R}+\frac{{\mu }_{0}I}{4\pi R}$ out of the paper.