Electric Charge

Sometimes when you rub two different materials together they attract each other. It only works for certain materials, and when the humidity is low.

Experiment: Try rubbing a balloon on your hair and then putting the balloon near an empty soda can. You are strongly encouraged to setup a race between two balloon powered soda cans.

Experiment: Try sticking 2 strips of scotch tape together and quickly peeling them apart. They should be attracted to each other. Repeat the experiment again to make 2 more strips. Some of the new tape will now repel the old tape.

These experiments can be explained if we imagine a substance called electric charge. When you rub some materials together the charge separates into 2 types. Each type of charge is attracted to the opposite type and repelled by the same type. It turns out those simple rules also explain electricity, chemical bonds, magnetism, and light!

opposite charges have an attractive force

negative charges have a repulsive force

positive charges have a repulsive force

neutral or balanced charges have no net force

If a positive and negative charge are close together the attractive and repulsive forces mostly cancel each other out. This explains why we don't notice the electrostatic forces until charges get separated.

Electric charge can't be created or destroyed. Like energy and momentum, electric charge is conserved.

The original evidence for this conservation law was based on repeated experiments. No one ever documented the total charge of a system increasing or decreasing. Charged particles can be created and destroyed, but only when another particle is created or destroyed to balance out the total charge.

symmetry and conservation laws

Conservation of charge, energy, and momentum are laws. Laws are just patterns we see when we collect data. We didn't have a explanation for these conservation laws until 1915 when Emmy Noether published a mathematical proof that conservation can be understood as a consequence of symmetry.

Symmetry is a property that doesn't change after a transformation. Charge is conserved because of a symmetry of electromagnetic fields called gauge invariance. This is a quantum mechanical principle related to magnitude and phase of a wave function.

There are a few different conservation laws in classical physics:

Conservation of energy occurs because of time symmetry. The laws of physics work the same at any time.

Conservation of momentum occurs because of translational symmetry. The laws of physics work the same anywhere in space.

Conservation of angular momentum occurs because of rotational symmetry. The laws of physics work the same at any angle.

Conservation of electric charge occurs because of gauge invariance. This is a quantum mechanical principle related to magnitude and phase of a wave function.

There are also a few more conservation laws in quantum mechanics: parity, lepton number, baryon number

You might have heard of conservation of matter, but matter isn't always conserved. You can destroy or produce matter by converting it into energy.

Elementary Electric Charge

Charge is measured in Coulombs (C). Charge increases the strength of the electrostatic force in the same way that more mass increases the strength of the gravitational force. We'll learn more when we study Coulomb's law.

In 1909 Robert Millikan and Harvey Fletcher performed the oil drop experiment to investigate electric charge. They sprayed a fine mist of oil into a uniform electric field. The electric field produced a force on some of the oil droplets. Based on that force, they found that charge only came in even multiples of about 1.6 × 10⁻¹⁹ C.

This evidence shaped the early model of the atom: negative electrons bound to a tiny nucleus of positive protons and neutral neutrons. Pretty much all charge that exists comes from electrons and protons, but there are some rare exotic charged particles.

electron
charge = −1.602 × 10⁻¹⁹ C
mass = 9.109 × 10⁻³¹ kg

proton
charge = +1.602 × 10⁻¹⁹ C
mass = 1.672 × 10⁻²⁷ kg

Example: These 6 values were recorded for electric charge. Which of the measurements are probably inaccurate? Why?

+3.2 × 10⁻¹⁹ C

−2.4 × 10⁻¹⁹ C

−8.0 × 10⁻¹⁹ C

+1.6 × 10⁻¹⁹ C

+5.2 × 10⁻¹⁹ C

−0.4 × 10⁻¹⁹ C

strategy

Charge only comes in even multiples of ±1.6 × 10⁻¹⁹ C.
You can't have half a charge, but you could have 3 charges.

solution

Charge has only been observed in packets of 1.602 × 10⁻¹⁹ C. Any recorded charge must be a multiple of this value.

$$\frac{3.2 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 2.0$$

$$\frac{2.4 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{1.5}$$

$$\frac{8.0 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 5.0$$

$$\frac{1.6 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = 1.0$$

$$\frac{5.2 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{3.25}$$

$$\frac{0.4 \times 10^{−19} \, \mathrm{C}}{1.6 \times 10^{−19} \, \mathrm{C}} = \cancel{0.25}$$

Example: How many electrons make up -4.5 C of charge?

solution

Use a conversion fraction with 1 electron and the charge on an electron.

$$-4.5 \, \mathrm{C} \left(\frac{1 \, \mathrm{e^-}}{-1.6 \times 10^{−19} \, \mathrm{C}}\right) = 2.81 \times 10^{19} \, \mathrm{e^-}$$

Example: How much charge would 234 trillion electrons have?

solution

$$234 \times 10^{12} \, \mathrm{e^-} \left(\frac{-1.6 \times 10^{−19} \, \mathrm{C}}{1 \, \mathrm{e^-}}\right) = -3.744 \times 10^{-5} \, \mathrm{C}$$

Conductivity

Conductive materials allow electric charges to easily move through them. Stuff related to the motion of charge is called electricity.

If a charge is applied to one part of a conductive material the charge will quickly spread out because like charges repel.

In some materials, current is understood as the flow of an electron hole. This model of current helps us understand the semiconductors used in solar panels, LEDs, and transistors.

These simulations don't include the nuances of quantum mechanics, they only show a cartoony approximation of conductivity.

In chemistry, elements are roughly divided into metals, metalloids and nonmetals. Metals are held together by loosely sharing their outer valence electrons. The cloud of free flowing electrons give metals most of their shared characteristics, like conductivity.

insulators
vacuum, nonmetals: gases, plastics, silk, fur

electrolytes
solvents with dissolved ions:
salt water, tap water, soda water

semiconductors
metalloids: carbon and silicon

conductors
metals, plasma

superconductors
certain low temperature ceramics

Question: Rank these substances by conductivity:

air, coca cola, copper, carbon, plastic fork

answer

high conductivity
copper (conductor)
carbon (semiconductor)
coca cola (electrolyte)
plastic fork (insulator)
air (insulator)
low conductivity

Question: Why are metals more conductive than nonmetals?

answer

In metals some electrons are free to move between atoms. In nonmetals the electrons are locked up in covalent bonds so they resist the electrostatic force.

Another way to make a substance conductive is to heat it up so much that electrons can leave the nucleus. We call this state of matter a plasma.

The positive charges on the left polarize the "atoms" on the right, but not enough to get the negative charges to jump over.

Question: Why can't the negative charges spread out into the positive charge group on the left?

answer

The electrostatic force follows a 1/r² rule, so it is weaker with distance. The negative charges would be more stable if they could join the positive charge, but the nearby positive charges have a stronger force.

Add a conductive for the negative charges.

Static Electricity

It's easy to separate a couple trillion electrons from their protons by walking with socks on a carpet. Lightning is produced in a similar way when a cloud with rising air ends up with an unbalanced distribution of charge.

Static electricity occurs when there is an imbalance of electrons and protons. A lasting charge separation can only occur in insulating materials, because in conductors positive and negative charges quickly pair up.

Static electricity effects are much stronger and longer lasting in low humidity. This is because water molecules increase the conductivity of air, allowing more separated charges to return.

Play around with this PhET simulation for static electricity.

Click to Run

Question: Which are conductors and which are insulators?
(balloons, sweater, wall, air)

answer

conductors: nothing in this simulation
insulators: balloon, sweater, wall, air

Question: Why do some electrons jump to the balloon from the sweater?
Why not the other way around?

answer

Some materials are better at holding onto extra electrons for complex quantum mechanical reasons.

Question: Why is the balloon attracted to the sweater after it gains some electrons?

answer

After rubbing, the balloon has unpaired negative charge, and the sweater has unpaired positive charge. Opposite charges attract.

Question: Why is the balloon attracted to the wall after it gains some electrons?

answer

After rubbing, the balloon has unpaired negative charge. When charge is near another insulator it repels the electrons enough that they are slightly farther away, but not enough to cause them to leave the nucleus. This charge separation is called polarization.

The polarization of the positive and negative pairs creates an induced charge. The charged balloon causes the wall to polarize, which increases the attraction and decreases the repulsion between the balloon and wall.

A TriboElectric Series lists which materials will become electrically charged after they are rubbed together.

Question: If you rubbed rubber on a cat, static electricity would cause them stick together. Which would gain a positive charge?

answer

The cat would end up with a positive charge. This means the cat would lose electrons to the rubber.

Question: Rubbing glass on PVC pipes can get super staticky. Use the TriboElectric series to decide which gets the positive charge.

answer

The glass would get the positive charge.

practice problems (11)

In case you wanted more practice I used AI to make some more problems. The rest of the site I made by hand, but generating endless problems seemed safe. I did find mistakes in the AI generated problems, and there are probably some I didn't find. Let me know if something could be fixed. I also added a practice problem on each page with no solution. That's intentional. Have fun!

printout.pdf show topics and mark harder problems

Question: Two plastic strips are rubbed with the same wool cloth on a dry winter day, and both strips gain electrons. Do the strips attract, repel, or have no electric force on each other?

answer

Both strips gained electrons, so both are negative. Like charges repel, so the strips push apart.

Example: On a dry winter day, a metal doorknob loses 2.5 × 10¹⁰ electrons to your hand. What is the doorknob's charge?

solution

Losing electrons leaves the doorknob with extra protons, so its charge is positive. Each electron that leaves takes away -1.60 × 10^-19 C.

$$2.5 \times 10^{10}\,\mathrm{e^-}\left(\frac{1.60 \times 10^{-19}\,\mathrm{C}}{1\,\mathrm{e^-}}\right)$$ $$4.0 \times 10^{-9}\,\mathrm{C}$$

That's +4.0 nC. Billions of electrons only add up to a few nanocoulombs, because each electron's charge is so small.

Example: A balloon rubbed on your hair ends up with a charge of -20 nC. How many extra electrons does it have?

solution

$$\mathrm{n} = 10^{-9}$$ $$-20\,\mathrm{nC} = -20 \times 10^{-9}\,\mathrm{C}$$
$$-20 \times 10^{-9}\,\mathrm{C}\left(\frac{1\,\mathrm{e^-}}{-1.60 \times 10^{-19}\,\mathrm{C}}\right)$$ $$1.25 \times 10^{11}\,\mathrm{e^-}$$

About 125 billion extra electrons came off your hair. Your hair is left with +20 nC, which is why it stands up and reaches toward the balloon.

Example: A tiny oil droplet in a charge experiment has a charge of +4.80 × 10^-18 C. How many electrons is the droplet missing?

solution

A positive charge means electrons are missing.

$$4.80 \times 10^{-18}\,\mathrm{C}\left(\frac{1\,\mathrm{e^-}}{1.60 \times 10^{-19}\,\mathrm{C}}\right)$$ $$30\,\mathrm{e^-}$$

The droplet is missing 30 electrons.

Example: A typical lightning bolt carries about 15 C of negative charge from a cloud to the ground. How many electrons is that?

solution

$$-15\,\mathrm{C}\left(\frac{1\,\mathrm{e^-}}{-1.60 \times 10^{-19}\,\mathrm{C}}\right)$$ $$9.4 \times 10^{19}\,\mathrm{e^-}$$

That's almost 100 billion billion electrons in a fraction of a second.

Example: A balloon with a charge of -32 nC touches a neutral metal sphere, and some of the balloon's charge moves onto the sphere. What charge does the sphere end up with?

solution

This cannot be solved from the information given. Charge is conserved, so whatever the sphere gains the balloon loses, but we don't know how much charge moved. That depends on things like how long they touched and how conductive the balloon's surface is. We only know the sphere's charge is negative and no more than 32 nC.

Example: In 1909, Robert Millikan measured the charges on tiny oil droplets. Suppose four droplets have charges of -3.2, -4.8, -8.0, and -11.2 × 10^-19 C. Show that each charge is a whole number of electrons. How many extra electrons does each droplet have?

solution

Divide each charge by the charge of one electron.

$$\frac{-3.2 \times 10^{-19}}{-1.60 \times 10^{-19}} = 2$$ $$\frac{-4.8 \times 10^{-19}}{-1.60 \times 10^{-19}} = 3$$

$$\frac{-8.0 \times 10^{-19}}{-1.60 \times 10^{-19}} = 5$$ $$\frac{-11.2 \times 10^{-19}}{-1.60 \times 10^{-19}} = 7$$

Every droplet has a whole number of extra electrons: 2, 3, 5, and 7. Millikan saw this pattern in thousands of measurements, which showed that charge comes in packets of 1.60 × 10^-19 C.

Example: A neutral sweater and a neutral balloon are rubbed together. The sweater loses 5.0 × 10¹¹ electrons to the balloon. What is the final charge on each?

solution

$$\text{sweater}$$ $$5.0 \times 10^{11}\,\mathrm{e^-}\left(\frac{1.60 \times 10^{-19}\,\mathrm{C}}{1\,\mathrm{e^-}}\right)$$ $$+8.0 \times 10^{-8}\,\mathrm{C}$$

$$\text{balloon}$$ $$5.0 \times 10^{11}\,\mathrm{e^-}\left(\frac{-1.60 \times 10^{-19}\,\mathrm{C}}{1\,\mathrm{e^-}}\right)$$ $$-8.0 \times 10^{-8}\,\mathrm{C}$$

The sweater is +80 nC and the balloon is -80 nC. The total is still zero, so charge was conserved. Rubbing moves charge, it doesn't create it.

Question: A comb is charged by running it through dry hair. It then picks up tiny bits of paper, even though the paper is neutral. Why?

answer

The charged comb polarizes the paper. If the comb is negative, it pushes the electrons in the paper slightly away, leaving the near side of each bit a little positive and the far side a little negative.

The positive side is closer to the comb, so its attraction is stronger than the repulsion on the farther negative side. The paper is pulled toward the comb, like the balloon sticking to the wall in the simulation on this page.

Example: A small bead starts with a charge of +2.40 × 10^-18 C. After rubbing, its charge is -8.00 × 10^-19 C. How many electrons did the bead gain or lose?

solution

$$\Delta q = q_f - q_i$$ $$\Delta q = (-8.00 \times 10^{-19}) - (2.40 \times 10^{-18})$$ $$\Delta q = -3.20 \times 10^{-18}\,\mathrm{C}$$
$$-3.20 \times 10^{-18}\,\mathrm{C}\left(\frac{1\,\mathrm{e^-}}{-1.60 \times 10^{-19}\,\mathrm{C}}\right)$$ $$20\,\mathrm{e^-}$$

The charge became more negative, so the bead gained 20 electrons. The first 15 cancel its positive charge, and the last 5 make it negative.

Example: A Van de Graaff generator's metal dome builds up a charge of +10 μC. How many electrons have been removed from the dome?

solution

$$\mu = 10^{-6}$$ $$10\,\mu\mathrm{C} = 10 \times 10^{-6}\,\mathrm{C}$$
$$10 \times 10^{-6}\,\mathrm{C}\left(\frac{1\,\mathrm{e^-}}{1.60 \times 10^{-19}\,\mathrm{C}}\right)$$ $$6.25 \times 10^{13}\,\mathrm{e^-}$$

That's enough charge to make your hair stand on end, but it's still only a tiny fraction of the dome's electrons.

Reading (5 minutes): Read Explainer: Ions and radicals in our world from Science News Explores. Then answer these questions.

What makes an ordinary atom electrically neutral?

answer

A neutral atom has equal numbers of positively charged protons and negatively charged electrons. The charges balance to zero overall.

What happens to an atom's net charge when it gains one or more electrons?

answer

It becomes negatively charged because it now has more electrons than protons. The charged atom is called a negative ion.

Why can salt water conduct electricity even though water itself is not a metal?

answer

Dissolved salts form mobile ions in the water. Those charged particles can move and carry electric current.