Question

$1m$ long wire is folded in the form of a circular coil and $100mA$ electric current is flowing in it, then magnetic field at a point $1m$ away from its centre on its axis :

• A. $\frac{{10}^{-5}}{4\pi }T$
• B. $\frac{{10}^{-8}}{2\pi }T$
• C. $\frac{{10}^{-5}}{2\pi }T$
• D. $\frac{{10}^{-8}}{4\pi }T$

Answer 1

The correct option is B $\frac{{10}^{-8}}{2\pi }T$

Given,

$i=100mA$

$x=1m$

The perimeter of the circular coil, $P=2\pi r$

$r=\frac{1}{2\pi }m$ , as $P=1$

The magnetic field at point $P$ is given by

$B=\frac{{\mu }_{0}i{r}^2}{2(r^2+x^2{)}^{2/3}}$

$B=\frac{4\pi \times {10}^{-7}\times 100\times {10}^{-3}\times (\frac{1}{2\pi }{)}^2}{2\left(\right(\frac{1}{2\pi }{)}^2+1^2{)}^{2/3}}$

$\left(\right(\frac{1}{2\pi }{)}^2+1^2{)}^{2/3}$ , it is approximately 1. Therefore,

$B=\frac{{10}^{-8}}{2\pi }T$

The correct option is B.