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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 B dl G G is perpendicular to B r B dl θ = G G B dl Brd rd θ I r dr π μ μ θ θ μ π π = = = G G v v 2 0 0 0 0 2 2 I I B dl d d I μ π = 0 2 I B r μ θ π = 0 2 I d 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. μ = G G v 0 enclosed B dl I Line integral Current outside the loop does not make a contribution: I = G G v Here 0 B dl Exercise: Prove it for the infinite straight wire. Calculating E and B fields πε = G 2 0 1 ˆ 4 q E r r Coulomb Law μ π × = G G 0 2 ˆ 4 v r B q r Biot-Savart Law Always true, can always use, but requires superposition: ε = G G enclosed closed 0 surface q E dA Gauss Law μ = G G v 0 enclosed B dl I Ampere’s Law Always true. Useful to get E or B 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
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Lecture 23 - Amperes law - Circulation around wire Draw an...

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