1/25/2008 j.velkovska 1 phys117b: lecture 8 more about electric potential equipotential lines ...

1/25/2008 J.Velkovska 1

PHYS117B: Lecture 8

More about electric potential Equipotential lines Relation between E and V

Capacitance

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Electric field lines

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Electric potential of a point charge

Potential is = 0 at infinity E goes as 1/r2 … V ~ 1/r ( last lecture we integrated

E to find V)

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Electric field and potential

, ,x y z

V V VE E E

x y z

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Topographic Maps and …pictures

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In Electrostatics, the peaks and valleys are created by charged objects

Density of lines indicates strength of E

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Electric potential inside a || plate capacitor

Uniform field =>

Equipotential lines are equally spaced

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More complex cases

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Calculating E from equipotential map

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Calculating E from V

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Capacitors and capacitance

Two conductors separated by an insulator or vacuum charged to +Q and –Q form a capacitor. Net charge on the capacitor is 0

Once the charge is established: potential difference between the two conductors

Potential difference means – you can store energy on the capacitor

Capacitance: measures the ability of the capacitor to store energy

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Capacitors can have any shape

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Capacitance depends on shape of the conductors and the medium

0 0

0

,

ab

QE

A

QdV Ed

A

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When we put a dielectric between the plates: E –weaker, V – smaller, C - larger

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Capacitors in series

1 21 2

1 21 2 1 2

,

1 1,

ac cb

ab

Q QV V V V

C C

Q Q VV V V

C C Q C C

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Capacitors in parallel