Question

What will be the magnetic field at point $P$ in the figure below?

• A. $\frac{\mu _{0} i}{4 R}\frac{3}{4}$
• B. $\frac{\mu_0 i}{4 R}\left(\frac{2}{\pi}+1\right)$
• C. $ \frac{\mu_0 i}{2 R}\left(\frac{2}{\pi}+1\right)$
• D. $\frac{2 \mu_0 i}{2 R}\left(\frac{2}{\pi}+1\right)$

Answer 1

Answer: (B)

Field due to section 1
$\overset{ \rightarrow }{B}_{1}=\frac{\mu _{0} i}{4 \pi R}$ upwards
field due to section 2
$\vec{B}_2=\frac{\mu_0 i(\pi)}{4 \pi R}=\frac{\mu_0 i}{4 R}$ upwards
Field due to section 3
$\overset{ \rightarrow }{B}_{3}=\frac{\mu _{0} i}{4 \pi R}$ upwards
therefore
$\overset{ \rightarrow }{B}_{n e t}=\overset{ \rightarrow }{B}_{1}+\overset{ \rightarrow }{B}_{2}+\overset{ \rightarrow }{B}_{3}$ upwards
$\overset{ \rightarrow }{B}_{n e t}=\frac{\mu _{0} i}{4 \pi R}+\frac{\mu _{0} i}{4 R}+\frac{\mu _{0} i}{4 \pi R}$ upwards
$\vec{B}_{\text {net }}=\frac{\mu_0 i}{4 R}\left(\frac{2}{\pi}+1\right)$ upwards