Question

Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires.

• A. $\frac{\mu_0 i}{2 r}\left(1+\frac{1}{\pi}\right)$
• B. $\frac{\mu_0 i}{2 r}\left(1+\frac{2}{\pi}\right)$
• C. $\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{\pi}\right)$
• D. $\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$

Answer 1

Answer: (D)

$B_{ P }=\left(\frac{\mu_0 i}{4 r}+\frac{\mu_0 i}{4 \pi r}\right)=\frac{\mu_\theta i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$