Lecture 4Electric Charge Coulomb’s Law

Gecko

Electric charge

The facts

When some objects are rubbed with fur, tissue paper, certain fabrics, etc, they sometimes attract or repel each other. The repulsive/attractive force depends on the distance between the objects, on the materials used, on how hard you rub…

DEMO: Rods, balloons…

The proposed model

Benjamin Franklin proposed that with the rubbing, objects acquired some kind of “electric charge”. There are two types of electric charge, which he called positive and negative.

The force works in the following way:

equal charges repel each other opposite charges attract each other the force gets weaker as the distance between the charged objects increases

Structure of matter

Later on it was established that matter is made of electrons, protons and neutrons.

➝ neutrons have no charge so we won’t worry about them

➝ protons are positive and are more or less fixed in their position

➝ electrons are negative and some of them are more of less free to move around.

Most of the time, # of protons = # of electrons, so objects are neutral.

Charging an object

When you rub a rod with a fur, a fraction of the surface electrons in one object is transferred to the other object.

Gain (loss) of electrons is equivalent to loss (gain) of protons. (This is not what usually happens, but sometimes it is easier to think it this way).

Gain of electrons → negatively charged objectLoss of electrons → positively charged object

-+++

--+ +

--Negative

rod Positive fur

Example:

Conductors, insulators

How free to move are the charge carriers? It depends on the material.

Examples of good conductors: Most metals, solutions of salts (like tap water)…Examples of good insulators: Plastics, rubber, glass, wood, air, pure water…

But… there is no perfect conductor or perfect insulator…

When they can move easily, we call the material a conductor. When they cannot move easily, we call it an insulator.

Positive

Negative

Neutral

disk

Gold leaves (or vane)

The electroscope

Electroscope

DEMO: Electroscope

Positive

Negative

Neutral

Charged rod

Induced + charge

Induced - charge

+

+

++

++ +

-+-

repulsion

--+

- - - -

-

-+-

+

-

-

This is called separation of

charge (or polarization) by

induction

Positive

Negative

Neutral

Stronger repulsion

Charged rod (closer)

Positive

Negative

Neutral

repulsion

Charged rod

Positive

Negative

Neutral

No repulsion

If we ground the electroscope while the rod is there, the charges in the electroscope that were “escaping” from the rod flow to the ground.

Induced charge

Positive

Negative

Neutral

No repulsion

Then we cut the grounding…

Positive

Negative

Neutral

Repulsion

And remove the rod…

The electroscope is now charged.The charge spreads now all over the object.

Electroscope charged by induction

What happens if you bring a charged rod near a neutral insulator?

Neutral piece of insulating material

Neutral molecule

Initially (without the rod), everything is neutral:

Charges now are not free to move. They can move a little…

“Normal” molecule

Molecule near a negatively charged rod

(polarized molecule)

Piece of polarized

insulating material

Positive

Negative

Neutral

Polarized insulator

Overall, there is a slight accumulation of positive charge on one side and negative on the other side, but it’s much smaller than in conductors (with induction)

Positive

Negative

Neutral

DEMO:

Balloon that sticks to the wall

F+F-

|F-| < |F+ | because of the distances

Net attraction

Geckos

How: Their toes are covered with millions of “hairs” that accumulate electric charge.

Fact: Geckos can climb up incredibly smooth walls.

This charge polarizes any surface they are on.

The result: a net attractive force.

Van der Waals force

Two molecules polarize each other (small shifts in the electron cloud distribution).

Net attractive force

This force is rather weak, but it is the most important interaction in noble gases.

Bigger molecul

e

Charges are more separate

d

Larger force

between molecule

s

Harder to separate the

molecules

Boiling temperatures are larger for heavier noble gases.He: 4K Ne: 27K Ar: 87K Kr: 120K Xe: 165K Rd: 212K

Coulomb’s Law

1 22

ˆqqF k r

r

29

20

212

0 2

1 Nm8.99 10

4 C

C8.85 10

Nm

ek

➝ F increases

Charles Coulomb proposed that the law which describes the electric force is:

What happens when q1 increases in magnitude?➝ F increases

What happens when q1 flips sign? ➝ Direction of F is reversed

What happens when the charges get closer?

Example: Coulomb’s force

A. 8.3×104 C

B. 8.3×10-5 C

C. 8.3×10-7 C

D. 8.3×10-9 C

E. 8.3×10-11 C

Two identical charges are separated by 25 cm. If the force on one charge is 1000 N, what is the size of the charge?

2

2

2

25

29

2

(1000 N)(0.25 m) 8.3 10 C

Nm9 10

C

qF k

r

Frq

k

repulsion

We cannot tell whether + or -

Unlikely (very large)

EXAMPLE: Force on a charge

Two charges Q1 and Q2 are fixed on the x-axis as shown. Find the electrostatic force on each of them.

-1 2 -2 1 0

x (in m)Q1 = -2 mC Q2 = +4 mC

1 2on 2 by 1 2

ˆe

Q QF k i

r

attractionon 1 by 2F

on 2 by 1F

3 329

22

2 10 C 4 10 CNm ˆ9 10 C 4 m

i 3 ˆ4.5 10 N i

Direction from the figure

Two charges Q1 and Q2 are fixed on the x-axis as shown. Find the electrostatic force on each of them.

-1 2 -2 1 0

x (in m)Q1 = -2 mC Q2 = +4 mC

attractionon 1 by 2F

on 2 by 1F

1 2on 1 by 2 2

ˆe

Q QF k i

r

3 329

22

2 10 C 4 10 CNm ˆ9 10 C 4 m

i 3 ˆ4.5 10 N i

Direction from the figure

EXAMPLE: Two electrons

Compare the gravitational attraction and the electric repulsion of two electrons.

2 2

2 2e e g

e mF k F G

r r

2

2

229 19

242

2211 31

2

Nm9.0 10 1.6 10 C

C 4.2 10

Nm6.7 10 9.1 10 kg

kg

e e

g

F k eF Gm

HUMONGOUS!!

19

31

1.6 10 C

9.1 10 kg

e

m

Electric forces are very strong

Electric forces are VERY strong. They are very much responsible for holding the universe together!!!

Electron-proton in an atomIonic crystalsCovalent bondsMetals

At distances < 10-17 m (within nuclei), the strong force takes over, but for anything >10-17m, electric force rules!