Question

Figure shows a straight wire of length l current i. The magnitude of magnetic field produced by the current at point P is

• A. $\frac{\sqrt{2}{\mu }_{0}i}{\pi l}$
• B. $\frac{{\mu }_{0}i}{4\pi l}$
• C. $\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$
• D. $\frac{{\sqrt{\mu }}_{0}i}{2\sqrt{2}\pi l}$

Answer 1

The correct option is C $\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$

As we know the general formula for finding the magnetic field due to a finite length wire

$B=\frac{{\mu }_0}{4\pi }\frac{i}{r}(sin{\varphi }_1+sin{\varphi }_2)$

Here ${\varphi }_1=0^o,{\varphi }_2={45}^o$

$\therefore B=\frac{{\mu }_o}{4\pi }\frac{i}{r}(sin{0}^o+sin{45}^o)$

$=\frac{{\mu }_o}{4\pi }\frac{i}{\sqrt{2}l}=\frac{\sqrt{2}{\mu }_{0}i}{8\pi l}$