-q +q

s

p

We can define a vector called the dipole moment (电矩 ).

Magnitude:

Direction: from the negative (-) charge to the positive (+) charge.

qsp

NOTE: This p has nothing to do with momentum!

304

1

r

pE

30

axis

2

4

1

r

pE

p

http://phet.colorado.edu/en/simulation/balloons

http://phet.colorado.edu/en/simulation/balloons

Why does the charged balloon stick to the neutral wall?

http://phet.colorado.edu/en/simulation/balloons

Neutral atom

+-

The atom becomes polarized.

++-

The atom becomes polarized.

++-

We can approximate the polarized atom as a dipole.

+ +-chargeE

p

chargeEp

This is the polarizability, which is different for every material.

The dipole makes an electric field at the charge.

+ +-chargeE

p

chargeEp

dipoleE

What is the force on the charge?

+ +-chargeE

p

dipoleE

rr

qE ˆ

4

12

0charge

+ +-chargeE

p

dipoleE

rr

qE ˆ

4

12

0charge

3

charge

03

0dipole

2

4

12

4

1

r

E

r

pE

Substitute…

+ +-chargeE

p

dipoleE

rr

qE ˆ

4

12

0charge

rr

qE ˆ

2

4

15

2

0dipole

Substitute…

+ +-chargeE

p

dipoleE

rr

qEqF ˆ

2

4

15

22

0dipolecharge

The charge is attracted to the polarized atom, no matter if the charge is positive or negative!

Wall

Balloon------

--

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

(1) The charges on the balloon polarize the wall.

Wall

Balloon------

--

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

+ -

(2) The polarized atoms in the wall attract the balloon.

The wall and the balloon are both insulators (绝缘材料 , or 电价值 ).

In an insulator, the charges are not free to move around. Atoms can be polarized, but they do not change their position.

A material in which charges are free to move around is called a conductor (导体 ).

Example: Salt water (ionic solution 离子溶液 )

At equilibrium, the net field in a conductor must be zero.

The ions move with a speed v = uE, where u is called the mobility.

Example: A metalIn a metal, one or two electrons from every atom is free to move around. They form a sea of electrons.

appliedE

onpolarizatiE

The metal becomes polarized.

Example: A metalIn a metal, one or two electrons from every atom is free to move around. They form a sea of electrons.

Net field inside is zero.

The metal becomes polarized.

We will prove these later, using Gauss’ Law

Permanent dipoles in an electric field

+

-

Water is a permanent dipole

OH

H

E+-

p

F

F

In a uniform field, the net force on a dipole is zero:

0 FF

E+-

p

F

F

But the net torque around the dipole’s COM is not zero:

Ep

E+

- p

F

F

This torque will rotate the dipole until it is parallel with the field.

E+

- p

F

F

The dipole-field system has a potential energy:

EpU

dipole

Water

Balloon------

--

+-

+-

+-

+-

+-

+-

+-

+ -

+-

+-

Water

Balloon------

--

+ -

+ -

+ -

+ -

+ -

+ -+

-

+ -

+ -

+ -

Water is polarized by rotating the molecules.