Question

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

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

For the perpendicular distance $r$ from the lower end of the conductor the infinitely long straight conductor looks like semi infinite conductor.

therefore magnetic induction $B_i$ due to semi infinite conductor is half the magnetic induction of the infinite conductor ,

$\therefore B=B_i/2$

$\therefore B=\frac{1}{2}\frac{{\mu }_{o}i}{2\pi r}$

$\therefore B=\frac{{\mu }_{o}i}{4\pi r}$