Question

A current ‘i’ flows along an infinitely long straight conductor. If $r$ is the perpendicular distance of a point from the middle point of the conductor then the magnetic induction $B$ is given by :

• A. $B=\frac{{\mu }_0}{4\pi }\frac{2i}{r}$
• B. $B=\frac{{\mu }_0}{4\pi }\frac{i}{r}$
• C. $B=\frac{{\mu }_0}{4\pi }\frac{\pi i}{r}$
• D. $B=\frac{{\mu }_0}{4\pi }\frac{2\pi i}{r}$

Answer 1

The correct option is A $B=\frac{{\mu }_0}{4\pi }\frac{2i}{r}$

$B=\frac{{\mu }_o}{4\pi r}i(Cos{\theta }_1-Cos{\theta }_2)$
for infinite long wire, ${\theta }_1=0$ and ${\theta }_2=180$
$\therefore B=\frac{{\mu }_o}{4\pi }\frac{2i}{r}$