Question

Figure shows a straight wire length $l$ carrying current $i$. The magnitude of magnetic field produced by the current at point $P$ is.

• A. $\frac{\sqrt{2{\mu }_{0}i}}{\pi 1}$
• B. $\frac{\sqrt{{\mu }_{0}i}}{4\pi 1}$
• C. $\frac{\sqrt{2}{\mu }_{0}i}{8\pi 1}$
• D. $\frac{{\mu }_{0}i}{2\sqrt{2}\pi 1}$

Answer 1

Answer: (C)

The given situation can be redrawn as follows. As we know the general formula for finding the magnetic field due to a finite length wire

$B=\frac{{\mu }_0}{4\pi }\cdot \frac{i}{r}\left(\sin {\varphi }_1+\sin {\varphi }_2\right)$
Here, ${\varphi }_1=0^{\circ },\varphi =45^{\circ }$
$\therefore B=\frac{{\mu }_0}{4\pi }\cdot \frac{i}{r}\left(\sin 0^{\circ }+\sin 45^{\circ }\right)$
$=\frac{{\mu }_0}{4\pi }\cdot \frac{i}{\sqrt{2}L}$
$\Rightarrow B=\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$