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Lect_32 - Example The electric dipole Lecture 32 Electric...

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Lecture 32 Electric field lines. The electric dipole. Example: The electric dipole + - d + Q -Q Definition: Electric dipole moment p Q d = G G Direction: From – to + p G What happens to a dipole in an external electric field? An electric dipole is placed in a uniform electric field E ext . + - F = QE ext F = QE ext E ext ext sin into the page net d Q E τ θ = θ ext net p E τ = × G G G The CM of the dipole does not move but the dipole rotates. d 0 net F = θ E ext p
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+ - When the dipole rotates an angle d θ , the work done by the electric field is: dW d τ θ = For a finite displacement: θ θ θ θ θ θ = − = + = −∆ ext ext sin (cos cos ) f i i f W pE d pE U E ext ext sin into the page pE τ θ = p θ ext sin pE d θ θ = − d θ is out of the page ext ext cos U p E p E θ = − = − G G Dipole in a uniform electric field: ext ext net p E U p E τ = × = − G G G G G ext ext sin cos net pE U p E τ θ θ = = − G E ext - + p E ext - + p E ext - + p ext MAX 180 0 U pE U θ τ = = = = D ext min 0 0 U pE U θ τ = = = − = D ext 90 0 pE U θ τ = = = D
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