when should we use biot savart law and when should we use amperes circuitant law for finding B(magnetic field) as both can be used . thank you​

Dear student,
The Biot–Savart law is fundamental to magnetostatics, playing a similar role to Coulomb's law in electrostatics. It is an equation that describes the magnetic field generated by an electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The law is valid in the magnetostatic approximation and is consistent with both Ampère's circuital law. While Ampère's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop and is analogous to gauss s theorem in electrostatics.

So we can say that Biot-Savart law and Ampere's law, both help in finding magnetic field distributions, but Ampere's law takes symmetry into account as its a closed line integral. So if we know the symmetry of the distribution then ampere law come handy.
Regards

 

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