Question

A current i is flowing in a straight conductor of length L. The magnetic field at a point distant $\frac{L}{4}$ from its centre will be

• A. $\frac{4{\mu }_{0}i}{\sqrt{5}\pi L}$
  
• B. $\frac{4{\mu }_{0}i}{2\pi L}$
  
• C. $\frac{{\mu }_{0}i}{\sqrt{2}L}$
• D. $Zero$

Answer 1

The correct option is A $\frac{4{\mu }_{0}i}{\sqrt{5}\pi L}$




By using $B=\frac{{\mu }_0}{4\pi }.\frac{i}{a}(sin{\varphi }_1+sin{\varphi }_2)$
$\Rightarrow B=\frac{{\mu }_0}{4\pi }.\frac{i}{\left(L/4\right)}\left(2sin\varphi \right)$
Also $sin\varphi =\frac{L/2}{\sqrt{5}L/4}=\frac{2}{\sqrt{5}}$
$\Rightarrow B=\frac{4{\mu }_{0}i}{\sqrt{5}\pi L}$