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(32) Electric Field Lines and the Electric Dipole

# (32) Electric Field Lines and the Electric Dipole - Lecture...

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Lecture 32 Electric field lines. The electric dipole.

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Example: The electric dipole + - d +Q -Q Definition: Electric dipolemoment p Q d = r r Direction: From – to + p r
What happens to a dipolein an external electric field?

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An electric dipoleis placed in a uniform electric field E ext . + - F = QE ext F = QE ext E ext ext sin int o t he page net d Q E τ θ = θ ext net p E τ = r r r TheCM of the dipoledoes not movebut the dipolerotates. d 0 net F = θ E ext p
+ - When thedipolerotates an angled θ , the work done by theelectric field is: dW d τ θ = For a finitedisplacement: θ θ θ θ θ θ = - = + - = -∆ ext ext sin (cos cos ) f i i f W pE d pE U E ext ext sin int o t he page pE τ θ = p θ ext sin pE d θ θ = - d θ is out of thepage ext ext cos U p E p E θ = - = - r r

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Dipolein a uniform electric field: ext ext net p E U p E τ = = - r r r r r ext ext sin cos net pE U p E τ θ θ = = - r E ext - + p E ext - + p E ext - + p ext MAX 180 0 U pE U θ τ = = = = o ext min 0 0 U pE U θ τ = = = - = o ext 90 0 pE U θ τ = = = o Stable equilibrium Unstableequilibrium Maximum torque
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