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lect7_handout - Physics 202, Lecture 7 Todays Topics...

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1 Physics 202, Lecture 7 Today’s Topics ± Capacitance (Ch. 26) ± Energy stored in capacitors ± Dielectric and Capacitance ² Previews: Energy density, electric dipole moment, torques, dielectric material. ³ Extra topic: Particle Accelerators in 10 min. Lecture 6 Review: Charging A Capacitor ----------- + + + + + + + + +q -q -dq --------------------- ++++++++++++ +Q -Q Uncharged Charging Charged Δ V=q/C Δ V=Q/C ³ Electric potential energy gained: Î After charging the capacitor stores potential energy: U= ½ Q 2 /C du= Δ Vdq C Q dq C q dq V du U Q / 2 1 ) )( ( 2 0 = = Δ = = ∫∫ Lecture 6 Review: Discharging A Capacitor + + + + + + + + +q -q -dq -------------------- +++++++++++ +Q -Q Uncharged dis-Charging Charged Δ V=q/C Δ V=Q/C ³ Potential energy released: Î the originally charged capacitor has potential energy: U= ½ Q 2 /C du= Δ Vdq C Q dq C q dq V dU U Q / 2 1 ) ( 2 0 = = Δ = = Energy Stored In A Capacitor ³ Show that energy required to charge a capacitor to a charge Q is U= ½ C( Δ V) 2 Solution :See previous two slides Æ energy stored in a capacitor is U = ½Q 2 /C = ½ C( Δ V) 2 ³ Important: This energy is actually stored in the form of the electric field . ³ Energy density of an Electric Field: u E =U/volume=U/(Ad) = ½ Q 2 /(CAd) = ½ Q 2 /( ε 0 A 2 ) Î u E = ½ ε 0 E 2 +Q ++++++++++++++ ----------------------- -Q d E= σ/ε 0 E= 0 E= 0 E= 0 E= 0 Recall: Parallel-plate: C= ε 0 A/d
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2 Quick Quiz ± A parallel plate capacitor is holding a charge q. when the plates are pulled apart (i.e. d increases), what happens to the energy stored in it? 1. Increases 2 D pull Î 2. Decreases 3. Stays the same ------- + + + + + + + +q -q d pull Arguments: ² volume increases while E almost the same ² work done to it when being pulling apart Electric Dipole Moments ± Electric dipole moment p .
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lect7_handout - Physics 202, Lecture 7 Todays Topics...

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