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)

$\frac{\mu_0 i}{2 r}\left(\frac{1}{2}+\frac{1}{2 \pi}\right)$

Answer 2

$BP ​= (\frac{μ0i}{4r}+\frac{μ0i}{4πr}) = \frac{μθi}{2r}(\frac{1}{2}+\frac{1}{2π})$