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Lecture_13 - Biot-Savart Law for a Single Charge Electric...

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Biot-Savart Law for a Single Charge r r q E ˆ 4 1 2 0 πε = Electric field of a point charge: Moving charge makes a curly magnetic field: 2 0 ˆ 4 r r v q B × = π μ B units: T (tesla) = kg s -2 A -1 Jean-Baptiste Biot (1774-1862) Felix Savart (1791-1841) Nikola Tesla (1856-1943) m/s C m T 2 = 7 0 10 4 π μ
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Observing magnetic field around copper wire: Can we tell whether the current consists of electrons or positive ‘holes’? In some materials current moving charges are positive: Ionic solution “Holes” in some materials (same charge as electron but +) 2 0 ˆ 4 r r v q B × = π μ 2 0 ˆ 4 r r v e B × = π μ = μ 0 4 π e ( ) v ( ) × ˆ r r 2 Conventional Current The prediction of the Biot-Savart law is exactly the same in either case.
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2 0 ˆ 4 r r v e B × = π μ = μ 0 4 π e ( ) v ( ) × ˆ r r 2 Metals: current consists of electrons Semiconductors: n -type – electrons p -type – positive holes Most effects are insensitive to the sign of mobile charges: introduce conventional current : v nA q i q I = = Conventional Current Units: C/s A (Ampere) André Marie Ampère (1775 - 1836)
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Typical electron current in a circuit is ~ 10 18 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire? 3 28 10 4 . 8 × m n v nA = s electrons # A = π D 2 4 3.14 1 × 10 3 m ( ) 2 4 = 8 × 10 7 m 2 v = 10 18 s -1 nA 10 18 s -1 8.4 × 10 28 m 3 ( ) 8 × 10 7 m 2 ( ) = 1.5 × 10 5 m/s Typical Mobile Electron Drift Speed
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Superposition principle is valid 2 0 ˆ 4 r r v q B i × = Δ π μ × = Δ = Δ i i i r r v q B B 2 0 ˆ 4 π μ × = Δ i r r v q B 1 ˆ 4 2 0 π μ l nA r r v q B Δ × = Δ 2 0 ˆ 4 π μ v nA q i q I = = 2 0 ˆ 4 r r l I B × Δ = Δ π μ
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