Static Electricity

When you bring different objects together (and especially rub them to maximize their areas of contact), they change: in particular they attract each other.

We say that they become electrically charged, with one of them becoming positive and the other negative. (Benjamin Franklin: the glass is positive and silk negative; the plastic is negative and fur positive.)

Opposite charges attract. Like charges repel each other.

How much they attract or repel each other depends on separation: the closer they are, the more they repel.

2 Coulomb’s Law: F = kq1q2/r SI unit of charge: Coulomb (C) 2 2 2 So Coulomb’s constant k = Fr /q1q2 has units N⸱m /C Experimental k = 8.99 x 109 N⸱m2/C2

If both charges are positive or both negative, F is positive = repulsive If one is positive and one is negative, F is negative = attractive Static charge on a screen can move liquid crystals in the display around, messing it up. A van de Graaff generator has a belt that rubs against the base transferring a lot of (negative) charge to the ball and eventually to the girl’s hair, which repels itself. All matter contains atoms, which consist of negative electrons orbiting a tiny nucleus which contains positive protons and electrically neutral neutrons.

-19 The charge on the proton qproton = + 1.6 x 10 C = +e

-19 The charge on the electron qelectron = -1.6 x 10 C = -e

A neutral atom has an equal number of electrons and protons.

When you transfer charge from one material to another, you are transferring electrons (usually) or protons (sometimes in solutions).

Extra electrons (or too few protons): negatively charged Too few electrons (or too many protons): positively charged Electrons are held in a material because of their electrical (or in the context of atoms, chemical) potential energy. The more negative this potential energy, the more work is needed to get them to leave. However, different materials have different amounts of chemical potential energy, so if you bring them together, electrons will leave the material for which the potential energy is less negative and go to the material for which it is more negative.

However, because of their repulsion, too many electrons won’t go the same spot, so rubbing the materials, and increasing their contact areas, will increase the amount of charge transferred. Coulomb’s Law looks a lot like Newton’s Law of Gravity:

2 Coulomb: F = kq1q2/r 2 -11 2 2 Newton: F = Gm1m2/r , where Newton’s constant G = 6.67 x 10 Nm /kg but there are 3 important differences: 1) The gravitational force on an object is proportional to its mass, so because F = ma, all objects will accelerate together acted on by only gravity; this is not true for electricity. 2) Gravity is always attractive, whereas electricity can be attractive or repulsive. 3) On the atomic scale, electricity is much stronger: -27 -31 Consider the force between a proton (mP= 1.7 x 10 kg) and electron (me = 9.1 x 10 kg) 2 2 2 2 Felec/Fgrav = (ke /r ) / (Gmpme/r ) = ke /Gmpme (independent of r) = (9 x 109 NC2/m2)(1.6 x 10-19C)2 / [ 6.7 x 10-11 Nm2/kg2)(1.7 x 10-27 kg)(9.1 x 10-31 kg)] ≈ 2 x 1039 !!!!

Consequences: 1) Electrical forces are responsible for holding “small” materials together – e.g. all chemical and elastic forces are electrical but, because most materials are electrically neutral while gravity is always attractive: 2) Gravitational forces are responsible for astronomy – i.e. hold solar systems and galaxies together. Problem: In a hydrogen atom, an electron is orbiting a proton at a distance of 0.052 nm = 5.2 x 10-11 m. How fast is the electron moving?

The Coulomb force on the electron must provide the centripetal force that keeps it in its orbit: F = ke2/r2 = mv2/r v2 = ke2/(mr) = (9 x 109 Nm2/C2)⸱(1.6 x 10-19 C)2 / [(9.1 x 10-31 kg) (5.2 x 10-11 m)] = 4.9 x 1012 m2/s2 v = 2.2 x 106 m/s 2 Coulomb’s Law: F = kq1q2/r Since the force decreases with distance, charged objects can attract neutral objects:

The negative charges in the sock repel the electrons in the wall, so the nearby part of the wall will become positive. (We say that the wall is “polarized”.) Now the positive part of the wall is closer to the sock than the negative part, so there is a net attraction of the sock to the wall.

The electrical (or in the context of static charges, electrostatic) potential energy on a charge is proportional to the amount of charge. (Similarly, gravitational potential energy is proportional to mass.) The electrical potential energy/charge is called the voltage, and is measured in volts (V):

Voltage = potential energy/charge Volt = Joule/Coulomb

If an object is at a large positive voltage, it will repel positive charges (i.e. they want to leave) and attract negative charges (e.g. electrons).

If an object is at a large negative voltage, it will repel negative charges (e.g. electrons) and attract positive charges. Problem: An electron gun (called a cathode), which is at zero volts, releases electrons toward a target (called an anode) which is at +200 V. How fast will the electrons be when they hit the anode?

The potential energy of each electron will fall by ΔPE = eΔV = (1.6 x 10-19 C) (200 V) = 3.2 x 10-17 J

Therefore, their kinetic energy ½ mv2 increases by 3.2 x 10-17 J i.e. v2 = 2(3.2 x 10-17 J)/(9.1 x 10-31 kg) = 7.0 x 1013 (m/s)2 v = 8.4 x 106 m/s An object which stores electrostatic energy by holding separated + and – charges is called a capacitor. Most commonly, it consists of two parallel plates of conductors (materials on which electrons can move easily), one with missing electrons, i.e.positive charge, +Q, and the other with an equal number of excess electrons, i.e. negative charge, -Q. Usually an insulator (a material through which electrons cannot move) is placed between them; in addition to holding the plates apart, the insulator (called a dielectric) may decrease the potential energy (and voltage).

The potential energy will be proportional to (+Q)⸱(-Q), so the voltage will be proportional to Q: V = Q/C, Q = CV, where C is called the capacitance. (It is proportional to the area of the plates.) C is measured in “farads” (F): 1 F = 1C/V.

Typical capacitors used in electrical circuits have values measured in microfarads (1 μF = 10-6 F) or even picofarads (1 pF = 10-12 F). Problem: A 300 pF is connected to a 9 V battery. How much charge is on each plate of the capacitor, and how many electrons have been transferred from the positive to negative plate?

Q = CV = (300 x 10-12 F) ⸱(9V) = (2700 x 10-12 C) = 2.7 x 10-9 C

The number of electrons = Q/e = (2.7 x 10-9 C) / (1.6 x 10-19 C) = 1.7 x 1010 Exercises: 1. If two objects repel one another, you know they have like charges on them. But how would you determine whether they were both positive or both negative? 2. You have an electrically neutral toy that you divide into two pieces. You notice that at least one of those pieces has an electric charge. Do the two pieces attract or repel one another, or neither? 3. Suppose that you have an electrically charged stick. If you divide the stick in half, each half will have half the original charge. If you split each of these halves, each piece will have a quarter of the original charge. Can you keep on dividing the charge in this manner forever? If not, why not? 4. A Ping-Pong ball contains an enormous number of electrically charged particles. Why don’t two Ping-Pong balls normally exert electrostatic forces on each other? 5. In industrial settings, neutral metal objects are often coated by spraying them with electrically charged paint or powder particles. How does placing charge on the particles help them to stick to an object’s surface? 6. The paint or powder particles discussed in Exercise 5 are all given the same electric charge. Why does this type of charging ensure that the coating will be highly uniform? 7. If the forces between electric charges didn’t diminish with distance, an electrically charged balloon wouldn’t cling to an electrically neutral wall. Why not? Problems: 3. If you were to separate all the electrons and protons in 1 g (0.001 kg) of matter, you’d have about 96,000 C of positive charge and the same amount of negative charge. If you placed these charges 1 m apart, how strong would the attractive forces between them be? 6. The upward net force on the space shuttle at launch is 10,000,000 N. What is the least amount of charge you could move from its nose to the launch pad, 60 m below, and thereby prevent it from lifting off?