Question

Two infinitely long wires each carrying the current I along the same direction are made into the geometry as shown in the figure. The magnetic field at the point P is?

• A. $\frac{{\mu }_{o}I}{\pi r}$
• B. $\frac{{\mu }_{o}I}{r}\left(\frac{1}{\pi }+\frac{1}{4}\right)$
• C. Zero
• D. $\frac{{\mu }_{o}I}{2\pi r}$

Answer 1

Answer: (A)

$\frac{{\mu }_{o}I}{\pi r}$

From ampere circuital law,

$\varphi \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$

Since net distance covered by current of the loop $=\frac{\pi r}{2}+\frac{\pi r}{2}=\pi r$

$⟹B\varphi dl=\mu +0I$

$⟹B\left(\pi r\right)={\mu }_{0}I⟹B=\frac{{\mu }_{0}I}{\pi r}$