Q. Figure shows a straight wire of length $l$ carrying current $i$. The magnitude of a magnetic field produced by the current at point $P$ is
A) $\frac{\sqrt{2}\mu_{0}i}{\pi l}$
B) $\frac{\mu_{0}i}{4\pi l}$
C) $\frac{\sqrt{2}\mu_{0}i}{8\pi l}$
D) $\frac{\mu_{0}i}{2\sqrt{2}\pi l}$
Explanation
(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
$B = \frac{\mu_{0}}{4\pi}.\frac{i}{r}(\sin\phi + \sin\phi_{2})$
Here $\phi_{1} = 0{^\circ},\ \phi = 45{^\circ}$
$\therefore B = \frac{\mu_{0}}{4\pi}.\frac{i}{r}\left( \sin{0{^\circ}} + \sin{45{^\circ}} \right) = \frac{\mu_{0}}{4\pi}.\frac{i}{\sqrt{2}l} \Rightarrow B = \frac{\sqrt{2}\ \mu_{0}i}{8\pi l}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.