Lecture-11-02-19-08

Lecture-11-02-19-08 - Lecture-11 Force on an Electric...

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1 qB mv r r v m qvB ma F Larmor electron = = = 2 r Larmor B dt v dt dq F d B l Id F d r r r r r r × = × = B v q F r r r × = Lecture-11 Force on an Electric Current For a small current element, we have Electron’s Path in a Magnetic Field θ sin , IlB F or B l I F = × = r r r r
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2 Torque on a Current Loop where μ is the magnetic dipole moment of the N-turn rectangular loop: () sin 22 , , left right bb IaB IabB For N turn coil NIabB NIAB Or B τ ττ θθ θ τμ =+ = == r rr For single-turn coil, A NI r r =
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3 A Galvanometer => Voltmeter/Ammeter A DC Motor A Speaker
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4 Biot-Savart Law Current generates magnetic field, according to right-hand rule . 2 2 2 7 2 1 ˆ , ˆ 1 4 41 0 [ / ] : 11 ˆ 4 o o o dB I dl r Then Idl r const r Or r r where permeability const Tesla m A Compare with dq dE r r μ π μπ πε × = × = = r r r r r r r r r Biot-Savart Law
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5 () ( ) 2 / 3 2 2 2 2 / 3 2 2 2 2 0 2 / 3 2 2 2 2 2 2 2 2 // 2 2 4 4 4 cos x R IR B x R IR B d x R IR B x R R x R Rd I B dB B B o o o o + = + = + = + + = = = μ
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Lecture-11-02-19-08 - Lecture-11 Force on an Electric...

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