Physics · Ch 3 — Magnetism and Magnetic Effects of Electric Current
Magnetic Field Due to the Current Carrying Wire of Infinite Length Using Ampere's Law
Magnetic Field Due to the Current Carrying Wire of Infinite Length Using Ampere's Law
For an infinitely long straight wire carrying current , symmetry says must have the same magnitude everywhere on any circle of radius centred on the wire, and must point tangent to that circle. Choosing exactly such a circle (radius , centred on the wire) as the Amperian loop makes parallel to everywhere on the loop, so . Ampere's law then gives , i.e.
-- reproducing, in a single line, the result that took a full geometric Biot-Savart integration to derive in §3.8.2. …
What this figure shows. An infinitely long straight wire carries current I out of the page at a marked point O, and a circular Amperian loop of radius r is drawn centred on the wire, lying in the plane perpendicular to it. At a point A on the loop, the field vector dB is drawn tangent to the circle, and the unit vector n is drawn along the same tangent direction, showing that B is everywhere parallel to dl along this particular choice of loop -- which is exactly why this circular loop is the convenient (symmetric) choic …
What this figure shows. A long solenoid of length l, carrying current I through many closely-wound turns, is drawn with its external field lines curving from one end, around the outside, back into the other end -- exactly the same pattern of field lines as those of a bar magnet, with one end of the solenoid behaving as its north pole (labelled N) and the other a …