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

The Correct Option is D

Applying Biot-Savart’s Law: \[ B_p = \left( \frac{\mu_0 I}{4r} + \frac{\mu_0 I}{4\pi r} \right) = \frac{\mu_0 I}{2r} \left( \frac{1}{2} + \frac{1}{2\pi} \right) \]