Question

An infinitely long wire carries a current $I$ (as shown in the figure). Find magnetic field at point $P$.

• A. $\frac{{\mu }_{0}I}{2\pi a}$
• B. $\frac{\sqrt{2}{\mu }_{0}I}{4\pi a}$
• C. $\frac{{\mu }_{0}I}{4\pi a}$
• D. $\frac{{\mu }_{0}I}{4\sqrt{2}\pi a}$

Answer 1

The correct option is C $\frac{{\mu }_{0}I}{4\pi a}$

Magnetic field due to the segment $AB$ at $P$ is zero.
The segment BC is semi-infinite.
Magnetic field due to an infinite wire at a distance from the wire is $B=\frac{{\mu }_{0}I}{2\pi r}$
Magnetic field due to the semi-infinite wire is half of that due to the infinite wire.
Hence, $B=\frac{{\mu }_{0}I}{4\pi a}$ since a is the perpendicular distance of point $P$ from the wire $BC$