State and explain Biot-Savart law.

Explanation

Consider a very small element of length dl of a conductor carrying current (i). Magnetic induction due to small element at a point P distance r form the element. Magnetic induction (dB) is directly proportional to i) current (i) ii) Length of the element (dl) iii) sine angle between r and dl and iv) Inversely proportional to the square of the distance from small element to point P.
`dB prop (i d l sin theta)/(r^(2))`
`dB=(mu_(0))/(4pi). (i d l sin theta)/(r^(2))`
where `mu_(0)=` permeability in free space.
`(mu_(0))/(4pi)=10^(-7)" Wb "m^(-1) A^(-1)`
In vector form `d vec B=(mu_(0) i)/(4 pi)((vec(dt)xxvecr))/(r^(3))`