State Biot - Savart's law.

Explanation

The magnitude of magnetic field `vec(dB)` at a point P at a distance r from the small elemental length taken on a conductor carrying current varies
(i) directly as the strength of the current I
(ii) directly as the magnitude of the length element `vec(dl)`
(iii) directly as the sine of the angle ( say , `theta`) between `vec(dl)" and " hat r` .
(iv) inversely as the square of the distance between the point P and length element `vec(dl)`.
This is expressed as
`dB propto (Idl)/r^(2) sin theta`
`dB = K (Idl)/r^(2) sin theta`
where `K = mu_(0)/(4pi) ` in SI units and K = 1 in CGS units. Is vector notation,
`d vecB = ( mu_(0))/(4pi) (I vec(dl) xx hatr)/r^(2) `
Here vector `vec(dB)` is perpendicular to both I `vec(dl)` ( pointing the direction of current flow) and the unit vector `hatr` directed from `vec(dl)` toward point P .