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#Amp - re s Circuital Law

In other words, the line integral of the magnetic field around some circular loop , centred on a current carrying wire, and in the plane perpendicular to the wire, is equal to times the current flowing in the wire. Note that this answer is independent of the radius of the loop: i.e.. the same result is obtained by taking the line integral around any circular loop centred on the wire.

In 1826, Amp re demonstrated that Eq. (177 ) holds for any closed loop which circles around any distribution of currents. Thus, Amp re's circuital law can be written: The line integral of the magnetic field around some closed loop is equal to the times the algebraic sum of the currents which pass through the loop. In forming the algebraic sum of the currents passing through the loop, those currents which the loop circles in an anti-clockwise direction (looking against the direction of the current) count as positive currents, whereas those which the loop circles in a clockwise direction (looking against the direction of the current) count as negative currents.

Amp re's circuital law is to magnetostatics (the study of the magnetic fields generated by steady currents) what Gauss' law is to electrostatics (the study of the electric fields generated by stationary charges). Like Gauss' law, Amp re's circuital law is particularly useful in situations which possess a high degree of symmetry.