lecture4 - Physics 2102 Gabriela Gonzlez Physics 2102...

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Physics 2102 Electric fields Gauss’ law Physics 2102 Gabriela González Carl Friedrich Gauss 1777-1855
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Q r E = kQ r 2 λ= Θ/Λ r E = kQ r r 2 +( L /2) 2 = kl L r r 2 +( L /2) 2 λ= Θ/2Ρθ θ r = R E = kQ R 2 sin( q ) q = 2 kl R sin q θ λ= Θ/2πΡ r θ E = kQ R 2 cos q = 2 kl R cos q p r σ = Θ/πΡ2 E = 2 kQ R 2 1- r r 2 + R 2 ae è ç ö ø ÷ = s 2 e 0 1- r r 2 + R 2 ae è ç ö ø ÷
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Electric field lines and forces We want to calculate electric fields because we want to predict how charges would move in space: we want to know forces . The drawings below represent electric field lines . Draw vectors representing the electric force on an electron and on a proton at the positions shown, disregarding forces between the electron and the proton. e- p + p + p + e- e- p + e- (d) Imagine the electron-proton pair is held at a distance by a rigid bar (this is a model for a water molecule). Can you predict how the dipole will move?
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Electric charges and fields We work with two different kinds of problems, easily confused: Given certain electric charges , we calculate the electric field produced by those charges. Example: we calculated the electric field produced by the two charges in a dipole : Given an electric field , we calculate the forces applied by this electric field on charges that come into the field. Example: forces on a single charge when immersed in the field of a dipole: (another example: force on a dipole when immersed in a uniform field)
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Electric Dipole in a Uniform Field Net force on dipole = 0; center of mass stays where it is. Net TORQUE τ INTO page. Dipole rotates to line up in direction of E. | τ | = 2(QE)(a/2)(sin θ29 = (Qa)(E)sin θ = | p| E sin θ = |p x E| The dipole tends to “align” itself with the field lines. +Q -Q Uniform Field E Distance between charges = a θ QE QE ρ p ρ E Potential energy of a dipole = Work done by the field on the dipole: When is the potential energy largest?
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Electric Flux: Planar Surface Given: planar surface, area A
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lecture4 - Physics 2102 Gabriela Gonzlez Physics 2102...

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