Lecture_11 - Potential Difference in a Capacitor with...

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= Δ B A l d E V s K E Es V plates = = Δ s E plates = Q / A ( ) ε 0 Δ V = Es = Q / A ( ) K ε 0 s K V V vacuum insulator Δ = Δ Potential Difference in a Capacitor with Insulator
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+Q -Q s = Δ B A l d E V d K E plates = Q / A ( ) ε 0 insulator vacuum V V V Δ + Δ = Δ Potential Difference in Partially Filled Capacitor Δ V vacuum = Q / A ( ) ε 0 s d ( ) Δ V insulator = Q / A ( ) K ε 0 d Δ V = Q / A ( ) ε 0 s d 1 1/ K ( ) A B
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Energy can be stored in electric fields E one _ plate = Q / A ( ) 2 ε 0 (for small s ) F by _ plate = QE = Q Q / A ( ) 2 ε 0 Δ U el = W = F Δ s = Q Q / A ( ) 2 ε 0 Δ s U el = Δ 2 0 2 1 ε E volume Δ U el Δ volume ( ) = 1 2 ε 0 E 2 Field energy density: (J/m 3 ) Energy expended by us was converted into energy stored in the electric field Energy Density of Electric Field
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In a multiparticle system we can either consider a change in potential energy or a change in field energy ( but not both ); the quantities are equal. The idea of energy stored in fields is a general one: Magnetic and gravitational fields can also carry energy.
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