The Electric Force

Topics

• Electrical Forces• Electric Charges• Conservation of Charge• Coulomb’s Law• Conductors and Insulators• Superconductors• Charging• Charge Polarization• Electric Field• Electric Potential• Electrical Energy Storage

Electric Charge

• Recall that fundamental particles carry something called electric charge– protons have exactly one unit of positive charge

– electrons have exactly one unit of negative charge

• Electrical current is flow of charge (electrons)• Electromagnetic force is one of the basic interactions in nature

– like charges experience repulsive force

– opposite charges attracted to each other (like gravity)

Electrical Attraction

Charge Balance

• Neutral atoms made of equal quantities of positive and negative charges– Neutral carbon has 6 protons, 6 electrons, (& neutrons)

• Electrons can be stripped off atoms– Occupy the vulnerable outskirts of atoms

• Usually charge flows in such a way as to maintain neutrality– Excess positive charge attracts excess negative charge

“Electrostatic” Force

• Two charges, Q1 and Q2, separated by distance r exert a force on each other:

F = (k·Q1·Q2) / r2

• k is a constant (9109), Q is in Coulombs, r in meters– One unit of charge (proton) has Q = 1.610-19 Coulombs

• Looks a lot like Newton’s gravitation in form• Electron and proton attract each other 1040 times stronger

electrically than gravitationally!– Good thing charge is usually balanced!

Coulomb Law Illustrated

• Like charges repel• Unlike charges attract

– +

+ +r

If charges are of same magnitude (and same separation),all the forces will be the same magnitude, with differentdirections.

––

Coulomb Force Law, Qualitatively

• Double one of the charges– force doubles

• Change sign of one of the charges– force changes direction

• Change sign of both charges– force stays the same

• Double the distance between charges– force four times weaker

• Double both charges– force four times stronger

Charge Separation

• Can separate charges by rubbing:– feet on carpet

– atmosphere across ground

– silk on glass

– balloon on hair!

• Insulators keep charges where they are (no flow)• Conductors distribute charge equally on surface

•Electrons loosely bound = conductor

•Electrons tightly bound = insulator

•Semiconductors

•Super Conductors

Static Electricity

• Rubbing action redistributes charge (unbalanced)• If enough charge builds up, we get discharge• Air spark is actually due to “breakdown” of air

– neutral air molecules separate into ions (electrons are stripped away)

– current can then flow through the “plasma-fied” air

– In essence, air becomes a “wire” for a short bit

– this happens at 3 million volts per meter

• 1 cm spark then at 30,000 volts

• typical finger-spark may involve a few billion electrons

Lightning

• Lightning is an unbelievably huge discharge

• Clouds get charged through air friction

• 1 kilometer strike means 3 billion volts!

• Main path forms temporary “wire” along which charge equalizes

– often bounces a few times before equal

• Thunder is bang produced by the extreme pressure variations induced by the formation and collapse of the plasma conduit

Electric Charges

Charge polarization

Charge polarization

Electric Field• Can think of electric force as establishing “field” telling particles

which way to move and how fast

+

Electric “field lines” tell a positivecharge which way to move.

For example, a positive charge itselfhas field lines pointing away from it,because this is how a positively-charged“test-particle” would respond if placedin the vicinity (repulsive force).

+

Run Away!

Electric Charges

Electric Shielding

Electric Potential

Electric Potential

electric potential = electric potential energy/charge

Electrical Energy Storage

Class Problem

• Two oppositely charged particles, an alpha particle with two positive charges and a less-massive electron with a single negative charge are attracted to each other. Compared to the force that the alpha particle exerts on the electron, the electron exerts a force on the alpha particle that is:

a) greater

b) the same

c) less

The particle with the most acceleration is the:

d) alpha particle

e) electron

f) same for each

As the particles get closer to each other, each experiences an increase in:

g) force

h) speed

i) acceleration

j) all of these

k) none of these

Class Problem• The answers are b, e and j:

By Newton's 3rd Law, the particles pull on each other with equal and opposite forces. By Newton's 2nd Law, for the same force the particle with less mass undergoes more acceleration. By Coulomb's Law, as the separation distance is decreased, the force increases. By Newton's 2nd Law, as the force increases the acceleration increases. Since the particles accelerate toward each other, their speeds increase also.

Class Problem

• A thin stream of water bends toward a negatively charged rod. When a positively charged rod is placed near the stream, it will bend in the:

a) opposite direction

b) same direction

c) … but it won't bend at all

Class Problem

• The answer is b. If you answered a, you likely thought the bending was due to positively charged water. But the water, even with many ions, normally has no appreciable net charge. The interaction between the charged rod and the water stream is mainly due to the dipole nature of water molecules. H2O molecules are electric dipoles, positive on the hydrogen side and negative on the oxygen side. Like compasses that align along a magnetic field, H2Os align along the electric field of the nearby rod—whether the rod is negative or positive. For both magnets and charges, the closest aligned pole or charge is always opposite in sign. Opposites attract, so net attraction is the result.

Class Problems

To say that electric charge is quantized is to say that the charge on an object 1) will interact with neighboring electric charges. 2) is sometimes positive. 3) is a whole-number multiple of the charge of one electron. 4) can be neither created nor destroyed. 5) may occur in an infinite variety of quantities.

To say that electric charge is conserved is to say that electric charge 1) is a whole number multiple of the charge of one electron. 2) may occur in an infinite variety of quantities. 3) will interact with neighboring electric charges. 4) can be neither created nor destroyed. 5) is sometimes negative.

When a car is struck by lightning, the resulting electric field inside the car is 1) normally huge for a time longer than the lightning stroke itself. 2) normally huge, but for a brief time. 3) zero. 4) small enough to be safe for an occupant inside.

Class ProblemsAn uncharged pith ball is suspended by a nylon fiber. When a negatively charged rubber rod is brought nearby, without touching it, the pith ball

1) is repelled by the rod. 2) becomes charged by induction. 3) becomes polarized. 4) in unaffected. 5) None of the above choices are correct.

After a capacitor is fully charged, the total number of electrons it contains 1) is much greater. 2) is slightly greater. 3) is slightly less. 4) is much less. 5) remains unchanged.

When the distance between two charges is halved, the electrical force between the charges

1) halves. 2) quadruples. 3) doubles. 4) is reduced by 1/4.. 5) None of the above choices are correct.

Class Problems

A negatively charged rod is held near a metal can that rests on a dry wood table. If you touch the opposite side of the can momentarily with your finger the can is then

1) positively charged. 2) partially discharged. 3) completely discharged. 4) negatively charged. 5) discharged only on the side touched.

The electric field around an isolated electron has a certain strength 1 cm from the electron. The electric field strength 2 cm from the electron is

1) the same. 2) half as much. 3) twice as much. 4) four times as much. 5) None of the above choices are correct.

If you use 10 J of work to push a coulomb of charge into an electric field, its voltage with respect to its starting position is

1) more then 10 V. 2) less than 10 V. 3) 10 V. 4) None of the above choices are correct.

Class Problems

Two charges separated by one meter exert 1-N forces on each other. If the charges are pushed to 1/4 meter separation, the force on each charge will be

1) 4 N. 2) 8 N. 3) 16 N. 4) 2 N. 5) 1 N.

The electrical force on a 2-C charge is 60 N. What is the value of the electric field at the place where the charge is located?

1) 240 N/C 2) 20 N/C 3) 120 N/C 4) 60 N/C 5) 30 N/C

A proton and an electron are placed in an electric field. Which undergoes the greater acceleration?

1) proton 2) electron 3) Both accelerate equally. 4) Neither accelerates.