Question

Let a straight wire of length $l$ carries a current i. The magnitude of magnetic field produced by the current at point $P$ (as shown in figure) is

• A. $\frac{{\mu }_{0}i}{2\sqrt{2}\pi l}$
• B. $\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$
• C. $\frac{{\mu }_{0}i}{4\pi l}$
• D. $\frac{\sqrt{2}{\mu }_{0}i}{\pi l}$

Answer 1

The correct option is B $\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$

The magnetic field due to a finite length wire
$B=\frac{{\mu }_0}{4\pi }.\frac{i}{r}(\sin {\varphi }_1+\sin {\varphi }_2)$
Here, ${\varphi }_1=0^o$ and ${\varphi }_2={45}^o$
$\therefore B=\frac{{\mu }_0}{4\pi }\frac{i}{r}(\sin 0^o+\sin {45}^o)$
$=\frac{{\mu }_0}{4\pi }\frac{i}{r}\frac{1}{\sqrt{2}}$
$=\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$