Write Biot-Savart law in vector form and mention the direction of magnetic field. Which term in the law works as a vector source and produces the magnetic field? Mention one similarity and one dissimilarity, between Biot-Savart law for magnetic field and Coulomb's law for electrostatic field.

Explanation

In vector form, Biot-Savart.s law can be written as
`dBprop(ldIxxr)/(r^(3))=(mu_(0))/(4pi).(ldIxxr)/(r^(3))" "......(i)`
the direction of dB would be the direction of the cross-product vector `(dIxxr)`, which is represented by the right handed screw rule or right hand thumb rule. In this law, the term ld, i.e. the current carrying segment is the vector source and produces the magnetic field.
Simllarity between Biot-Savarts. Law and Coulomb.s Law
Both magnetic and electric fields at a point are inversely .proportional to the square of the distance between the field source and the point.
Dissimilarity between Biot-Savart.s Law and Coulomb.s Law
The source of electrostatic field is scalar in nature, whereas the source of magnetic field is vector in nature.