Question

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

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

Answer 1

Answer: (B)

Field due to section 1
${\overrightarrow{B}}_1=\frac{{\mu }_{0}i}{4\pi R}$ upwards
field due to section 2
${\vec{B}}_2=\frac{{\mu }_{0}i(\pi )}{4\pi R}=\frac{{\mu }_{0}i}{4R}$ upwards
Field due to section 3
${\overrightarrow{B}}_3=\frac{{\mu }_{0}i}{4\pi R}$ upwards
therefore
${\overrightarrow{B}}_{net}={\overrightarrow{B}}_1+{\overrightarrow{B}}_2+{\overrightarrow{B}}_3$ upwards
${\overrightarrow{B}}_{net}=\frac{{\mu }_{0}i}{4\pi R}+\frac{{\mu }_{0}i}{4R}+\frac{{\mu }_{0}i}{4\pi R}$ upwards
${\vec{B}}_{\text{net }}=\frac{{\mu }_{0}i}{4R}\left(\frac{2}{\pi }+1\right)$ upwards