Lecture 4 Electric 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 object Loss 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- |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 molecule Charges are more separated Larger force between molecules 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 ➝ F increases Charles Coulomb proposed that the law which describes the electric force is: What happens when q 1 increases in magnitude? ➝ F increases What happens when q 1 flips sign? ➝ Direction of F is reversed What happens when the charges get closer?

Example: Coulomb’s force A.8.3×10 4 C B.8.3×10 -5 C C.8.3×10 -7 C D.8.3×10 -9 C E.8.3× 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? repulsion We cannot tell whether + or - Unlikely (very large)

EXAMPLE: Force on a charge Two charges Q 1 and Q 2 are fixed on the x-axis as shown. Find the electrostatic force on each of them x (in m) Q 1 = -2 mC Q 2 = +4 mC attraction Direction from the figure

Two charges Q 1 and Q 2 are fixed on the x-axis as shown. Find the electrostatic force on each of them x (in m) Q 1 = -2 mC Q 2 = +4 mC attraction Direction from the figure

EXAMPLE: Two electrons Compare the gravitational attraction and the electric repulsion of two electrons. HUMONGOUS!!

Electric forces are very strong Electric forces are VERY strong. They are very much responsible for holding the universe together!!! Electron-proton in an atom Ionic crystals Covalent bonds Metals At distances m, electric force rules!