State Ampere's circuital law . Using it, derive the expression for magnetic field at a point due to a long current carrying conductor .

Explanation

Statement : The line integral of magnetic field around any closed path in free space is equal to `mu_0` times the net current enclosed by that path.
i.e., `ointvecB.dvecI=mu_0I`

Consider a infinitely long conductor carrying a current . Let `I_e` be the current enclosed by the loop and L be the length of the loop for which .B. is tangential , then the amperes circuital law `oint vecB.dvecI=mu_0I` becomes `BL=mu_0I`
If we assume a straight conductor and the boundary of the surface surrounding the conductor as a circle , then length of the boundary is the circumference , `2pir` , where .r. is the radius of the circle . Then B. `2pir=mu_0I`
`therefore B=(mu_0I)/(2pir)`