Question

A current $i$ ampere flows along a semiinfinite long straight conductor. If $r$ metre is the perpendicular distance of a point from the lower-end of the conductor, then the magnetic induction $B$ is given by :

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

Answer 1

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

Magnetic field $B=\frac{{\mu }_0}{4\pi r}I(\sin {\theta }_1+\sin {\theta }_2)$

For magnetic field at point B ${\theta }_2=\frac{\pi }{2}$, ${\theta }_1=0^0$
$\therefore B=\frac{{\mu }_0}{4\pi r}I(\sin 0^0+sin\frac{\pi }{2})=\frac{{\mu }_{0}i}{4\pi r}$