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2049_ch29B

2049_ch29B - Biot-Savart Law Deduced from many experiments...

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PHY2049: Chapter 29 1 Biot-Savart Law Î Deduced from many experiments on B field produced by currents, including B field around a very long wire ± Magnitude ± Direction: RHR #2 ± Vector notation ± Applications ² Reproduces formula for B around long, current-carrying wire ² B by current loop (on axis) ² In more complicated cases, numerically integrate to find B 2 0 sin 4 r θ ds i π μ dB = 3 0 4 r r s d i π μ B d r r r × = 1/r 2 depedence Like Coulomb’s law dB=0 ahead of ds and behind it. Maximum on plane perp. to ds.

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PHY2049: Chapter 29 2 Biot-Savart Law Ampere’s Law Proof of equivalence not in the book (Require vector calculus and relies on the absence of magnetic monopoles) equivalent Law of Magnetism Î Unlike the law of electrostatics, comes in two parts ± Part 1 Effect of B field on moving charge ± Part 2 Current produces B B v q F r r × =
PHY2049: Chapter 29 3 Î Radius R and current i: find B field at center of loop ± Direction: RHR #3 (see picture) Î If N turns close together Î

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2049_ch29B - Biot-Savart Law Deduced from many experiments...

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