lecture4

# lecture4 - Physics 2102 Gabriela Gonzlez Carl Friedrich...

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1 Physics 2102 Gabriela González Carl Friedrich Gauss 1777-1855 Q r E = kQ r 2 λ =Q/L r E = kQ r r 2 + ( L /2) 2 = k λ L r r 2 + ( L /2) 2 λ =Q/2R θ θ r = R E = kQ R 2 sin( θ ) = 2 k R sin θ λ =Q/2 π R r θ E = kQ R 2 cos = 2 k R cos π r σ =Q/ π R 2 E = 2 kQ R 2 1 r r 2 + R 2 Λ Ν Μ Ξ Π Ο = σ 2 ε 0 1 r r 2 + R 2 Λ Ν Μ Ξ Π Ο

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2 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 - 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? 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)
3 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 θ ) = (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 p E Potential energy of a dipole = Work done by the field on the dipole: When is the potential energy largest?

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lecture4 - Physics 2102 Gabriela Gonzlez Carl Friedrich...

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