Lecture 23 - Amperes law

Lecture 23 - Amperes law - Circulation around wire Draw an...

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1 Lecture 24 Ampère’s law Ampère s law Circulation around wire Draw an imaginary loop around a straight infinite wire and compute G G v Bdl G G is perpendicular to Br B dl θ ⋅= G G Brd rd I r dr π μμ θμ ππ = = ∫∫ G G v v 2 00 0 0 22 II d μ = 0 2 = 0 2 Ampère’s law This result turns out to be true for ANY loop around ANY current. We will not prove it in the general case. It is partially done in the book. G G v 0e n c l o s e d Line integral Current outside the loop does not make a contribution: G G v Here 0 Exercise: Prove it for the infinite straight wire. Calculating E and fields πε = G 2 0 1 ˆ 4 q Er Coulomb Law × = G G 0 2 ˆ 4 vr Bq Biot-Savart Law Always true, can always use, but requires superposition: ε G G enclosed closed 0 surface EdA Gauss Law G G v n c l o s e d Ampere’s Law Always true. Useful to get or when charge/current distributions are symmetric
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2 Direction of the Amperian loop Same right-hand rule as in the B -field handy-trick: 1) choose a direction for positive currents 2) thumb in this direction, 3) fingers give direction of loop dl μ ⋅= G G v 01 2 (-) Bdl I I
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This note was uploaded on 09/21/2011 for the course PHYS 222 taught by Professor Johnson during the Spring '07 term at Iowa State.

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Lecture 23 - Amperes law - Circulation around wire Draw an...

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