Question

A wire bent as shown in Figure carries a current $I$. Find the magnetic field at $P$ :

• A. $\frac{{\mu }_{0}I}{4R}$
• B. $\frac{3{\mu }_{0}I}{2R}$
• C. $\frac{7{\mu }_{0}I}{8R}$
• D. $\frac{{\mu }_{0}I}{8R}$

Answer 1

Answer: (D)

$\frac{{\mu }_{0}I}{8R}$

Magnetic field due to the two straight segments of length $l$ at point $P$ are zero respectively.
Magnetic field due to the quarter of circle is ${\frac{1}{4}}^{th}$ of that due to a circular coil.
Magnetic field due to a circular coil is $B=\frac{{\mu }_{0}I}{2R}$ where I is current in the coil and $R$ is the radius of the coil.
Hence magnetic field at $P$ due to the quarter segment is $B=\frac{1}{4}\times \frac{{\mu }_{0}I}{2R}=\frac{{\mu }_{0}I}{8R}$