Discuss similarities and differences of Biot Savart law with Coulomb's law.

Explanation

1. Similarities and differences of Biot-Savart.s law with Coulomb.s law are as below.
2. Similarities :
(1) Both depend inversely on the square of distance.
(2) Both are long range.
(3) The principle of superposition applies to both fields.
Thus, static electric field `E=(kQ)/r^(2)`
`thereforeEpropQ`
Similarly for Biot-Savart law,
`B=mu_(0)/(4pi)(Idlxxhatr)/r^(2)`
`thereforeBpropIdl`
3. Differences :
(1) Magnetic field is produced due to vector component `Idvecl`. Whereas electric field is produced due to scalar component dq.
(2) The electrostatic field is along the displacement vector joining the source and the field point, whereas, the magnetic field is perpendicular to current element `Idvecl` and the plane containing the displacement vector `vecr`.
(3) Biot-Savart.s law is depend on angle `(sintheta)`. The point on `Idvecl` element be `theta=0^(@)` so that `sin0^(@)=0` and no magnetic field on axial point whereas Coulomb.s law does not depend on angle `theta`.