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 pealing 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 patterns we see when we collect data. We didn't have a explanation for why until 1915 when Emmy Noether published a mathematical proof that conservation can be understood as a consequence of symmetry. Charge is conserved comes from the symmetry of electromagnetic fields.

Symmetry is a property that doesn't change after a transformation. If you translate (move) your location in space the total momentum of a system of particles doesn't change. So we say that momentum is conserved.

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 mass, but mass isn't always conserved. You can destroy or produce mass because mass is a type of energy.

    Elementary Electric Charge

    Charge is measured in Coulombs (C). Coulomb's increase 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.

    low high conductivity high low resistance

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

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

    semi-conductors
    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 (semi-conductor)
    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.

    Balloons and 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 polystyrene foam (styrofoam) 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 styrofoam.

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

    The glass would get the positive charge.