Question
Wed November 02, 2011 By: Hussain Shaikh

what is relation between gauss & ampere circuital law,& also between coulombs law & bio savart law?

Expert Reply
Thu November 03, 2011
Ampere circuital law is analogous to Gauss's law. Ampere's law is a relationship between the tangential component of magnetic field at points on a closed curve and the net current through the area bounded by the curve.
Consider a long straight conductor carrying a current passing through the centre of a circle of radius r in a plane perpendicular to the conductor.
Using Biot Savart's law we know already that the field at a distance r is

the field at all points on the circle and the direction is given by the tangent drawn to the circle at that point.

i.e., the flux is equal to the times the current threading through the area bounded by the circle. Hence, Ampere circuital law can be stated as follows

"The line integral of the magnetic field B around any closed path is equal to m0 times the net current across the area bounded by the path."

The magnetic field B as computed from the Biot–Savart law will always satisfy Ampère's circuital law

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