Find the magnetic induction due to a long current carrying conductor.

Explanation

Consider a long straight conductor carrying a current i. Let P be a point at a distance r from the conductor. Let r be the radius of the circle passing through point p. Magnetic induction is same at all points on the circle. Consider a small element of length dl.
`oint vecB. vec(dl)=oint B dl cos =theta`
Angle between B and dl is zero i.e. `theta=0`
`=B oint dl`
`oint vecB. vecdl = B (2 pi r) rarr (1)` According to Ampere's laws
`oint vecB. vec(dl)=mu_(0)i rarr (2)`
From equations (1) and (2), `B(2 pi r)=mu_(0)i`
`B=(mu_(0)i)/(2 pi r)`