State and explain Ampere's law.

Explanation

Ampere's law: The line integral of the intensity of magnetic induction field around closed path is equal to `mu_(0)` times the net current (i) enclosed by the path.
`ointvecB.vec(dl)=mu_(0)i`
Proof : Consider a long straight conductor carrying current i as shown in figure. Magnetic induction at a distance r from the conductor is given by
`B=(mu_(0)i)/(2 pi r)` (From Biot-Savart's law) The value of B is same at all points on the circle.
`oint vecB. vec(dl)=oint B d l cos theta.`
`=B oint dl = B xx 2 pi r" "(because theta=0^(@)" Angle between "vecB & vec (dl)" is zero")`
`=(mu_(0)i)/(2 pi r)xx2pi r`
`oint vecB. vec(dl)=mu_(0) i`
This proves Ampere's circuital laws.