Question

Using Ampere's circuital law, obtain an expression for the magnetic flux density 'B' at a point 'X' at a perpendicular distance 'r' from a long current carrying conductor.(Statement of the law is not required).

Answer 1

Let $MN$ be a long straight wire carrying current and $P$ a point at distance ${}^{\prime }{a}^{\prime }$ from wire where magnetic field $B$ has to be found

using Ampere's circuital law, let us consider a circle element $dl$ at $P$

$\Rightarrow \oint B.dl={\mu }_{0}I$

$B$ is constant everywhere on the loop

$\Rightarrow B\oint dl={\mu }_{0}I$

$\Rightarrow B\times 2\pi a={\mu }_{0}I$

$\Rightarrow B=\left(\frac{{\mu }_0}{4\pi }\right)\times \frac{2I}{a}$