Electric FieldPoint charge:

Dipole: for r>>s :at <r,0,0>

at <0,r,0>

+q-qs

x

y

z at <0,0,r>

Dipole moment: p = qs

Uniformly charged sphere:

for r>R (outside)

for r<R (inside)

What is the magnitude of the net electric field at location X, due to these two charges? Assume d >> s

Clicker Question 1

+2e-e

sd X

Choice

A

B

C

What is the approximate magnitude?

Choice

A

B

C

Clicker Question 2 Locations A, B, and C are equidistant from the center of the dipole (charges +q and –q are separated by s). At which location(s) is the magnitude of the electric field approximately ?

A. at location A

B. at location B

C. at location C

D. at locations A, C

E. at locations A, B, C

+A

C

d

d

-

d

B

What is the direction of the electric field at location X, due to the dipole?

Clicker Question 3

A

CB

E

D

-

+

X

Clicker Question

Clicker Question

Clicker Question

Choice of System

Multiparticle systems: Split into objects to include into system and objects to be considered as external.

To use field concept instead of Coulomb’s law we split the Universe into two parts:

• the charges that are the sources of the field

• the charge that is affected by that field

• Convenience: know E at some location – know the electric force on any charge:

Example: if E > 3106 N/C air becomes a conductor• Retardation

Nothing can move faster than light cc = 300,000 km/s = 30 cm/ns

• Electric properties of matter– independent of how this field was produced.

Coulomb’s law is not completely correct – it does not contain time t nor speed of light c.

rr

qE ˆ

4

12

0

r

r

qqF ˆ

4

12

21

0

v<<c !!!

F q

rE

A Fundamental Rationale

Chapter 15

Matter and Electric Fields

Matter is made out of atoms.

Atom contains charged particles: electrons (-e), protons (+e)Neutral atom: number of electrons and protons is equal:

Example: Hydrogen atom: 1 proton, 1 electron net charge = (+e) + (-e)=0

Sodium atom: 11 protons, 11 electrons

Sodium atom (Na) can lose an electron: Sodium ion (Na+): (+11e) + (-10e) = +e

Ordinary matter is electrically neutral.However, can be charged by adding/removing charged particles

Net Charge

The net charge of a system and its surroundings cannot change

If one object gets charged positively, there must be an object which gets charged negatively.

Conservation of Charge

The net electric charge is conserved in any physical process.

Charge can be transferred from one object to another.

Pair-Production:

10-10 m (1 Å)

Nucleus, ~10-15 m

Charge of electron cloud equals that of nucleus neutral atom.

If the electron cloud is centered on the nucleus electric field produced by electrons exactly cancels the field produced by nucleus.

Hydrogen

The Structure of an Atom

+E

Force due to E created by positive charge shifts electron cloud and nucleus in opposite directions: electric dipole.

An atom is said to be polarized when its electron cloud has been shifted by the influence of an external charge so that the electron cloud is not centered on the nucleus.

+-

Polarization of Atoms

• it is not a permanent dipole

E

• an induced dipole is created when a neutral object is polarized by an applied electric field

An applied electric field creates induced dipoles!

Induced Dipole

Polarization

Amount of polarization p in most materials is proportional to the magnitude of the applied electric field:

- “polarizability” of a material

In an induced dipole, is the distance between the charges fixed?The distance is proportional to the strength of the applied field.

+¿ −+¿

E

−+¿

E

1. Charge q1 creates field E1 at the location of the atom

A Neutral Atom and a Point Charge

2. Field E1 polarizes the atom creating a dipole

1)

A Neutral Atom and a Point Charge

3. Dipole creates field E2 at the location of q1

1)

2)

A Neutral Atom and a Point Charge

4. Induced dipole exerts force F1 on the charge:

1)

2)

3)

A Neutral Atom and a Point Charge

5. The charge q1 exerts force F2 on the dipole (reciprocity):

1)

2)

3)

4)

A Neutral Atom and a Point Charge

1)

2)

3)

4)

5)

Neutral atoms are attracted by charges!Interaction strength ~ 1/r5

A Neutral Atom and a Point Charge

Atom A is easier to polarize than atom B. Which atom would experience a greater attraction to a point charge a distance r away?

+-

+-A

B

FA

FB

Exercise

Interaction of Charged Tapes and Neutral Matter

Repulsion:

FR

Attraction:

FA

Total:

q1 q2

Interaction of like-charged Objects

Conductor Plastic

Suppose tape is negatively charged, and you rub a wooden pencil on a wool sweater and bring it near the tape.

If tape swings toward the pencil, does it show that the pencil had been charged positively?

NOT NECESSARILY!

-

--

--

Attraction: can happen for like-charged objects!

Repulsion: can happen only for like-charged objects!

Determining the Charge of an Object

F F

The field appears to be weaker in presence of intervening (polarizable) object. Both tapes are attracted to paperSuperposition principle: the presence of matter does not affect the electric field produced by a charged object.

Intervening matter does not “block” the E field

The resulting field is a superposition of two fields: Field of the other charge plus the field of induced dipoles.

Electric Field Through Intervening Matter