1/25/2008 J.Velkovska 1

PHYS117B: Lecture 8

More about electric potential Equipotential lines Relation between E and V

Capacitance

1/25/2008 J.Velkovska 2

Electric field lines

1/25/2008 J.Velkovska 3

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)

1/25/2008 J.Velkovska 4

Electric field and potential

, ,x y z

V V VE E E

x y z

1/25/2008 J.Velkovska 5

Topographic Maps and …pictures

1/25/2008 J.Velkovska 6

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

Density of lines indicates strength of E

1/25/2008 J.Velkovska 7

Electric potential inside a || plate capacitor

Uniform field =>

Equipotential lines are equally spaced

1/25/2008 J.Velkovska 8

More complex cases

1/25/2008 J.Velkovska 9

Calculating E from equipotential map

1/25/2008 J.Velkovska 10

Calculating E from V

1/25/2008 J.Velkovska 11

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

1/25/2008 J.Velkovska 12

Capacitors can have any shape

1/25/2008 J.Velkovska 13

Capacitance depends on shape of the conductors and the medium

0 0

0

,

ab

QE

A

QdV Ed

A

1/25/2008 J.Velkovska 14

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

1/25/2008 J.Velkovska 15

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

1/25/2008 J.Velkovska 16

Capacitors in parallel