Chapter 21: Electric Charge and Electric Field Notes

Electric Charge

  • Electrostatics involves interactions between electric charges at rest or nearly so.
  • Like charges repel, and unlike charges attract.
  • There are two types of electric charge: positive and negative.

Electric Charge and Structure of Matter

  • Atoms consist of:
    • Negative electrons
    • Positive protons
    • Uncharged neutrons
  • Protons and neutrons form the nucleus.
  • The nucleus is surrounded by electrons.

Atoms and Ions

  • A neutral atom has an equal number of protons and electrons.
  • Positive ions have had one or more electrons removed.
  • Negative ions have an excess of electrons.

Conservation of Charge

  • Protons and electrons have the same magnitude of charge.
  • The magnitude of charge of an electron or proton is a natural unit of charge, and all observable charge is quantized in this unit.
  • The principle of charge conservation: The algebraic sum of all electric charges in a closed system is constant.

Conductors and Insulators

  • Conductors allow charge to move freely (e.g., copper).
  • Insulators do not allow charge to move freely (e.g., nylon).

Charging by Induction (4 Steps)

  1. Start with an uncharged metal ball on an insulating stand.
  2. Bring a charged rod near the ball; free electrons in the ball are repelled and shift away from the rod.
  3. While the rod is nearby, touch a conducting wire to the ball and ground it.
  4. Disconnect the wire, then remove the rod, leaving a net positive charge on the ball.

Electric Forces on Uncharged Objects

  • Charged objects can exert forces on uncharged objects.
  • Polarization: A slight shifting of charge within the molecules of a neutral insulator.
  • A charged object of either sign attracts a neutral insulator.

Electrostatic Painting

  • Induced charge attracts charged paint droplets to a metal object.

Measuring Electric Force Between Point Charges

  • Coulomb studied interaction forces of charged particles in 1784 using a torsion balance.
  • The electric force is inversely proportional to the square of the distance between charges.

Coulomb's Law

  • The magnitude of the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
  • Coulomb's Law Equation: F=kq<em>1q</em>2r2F = k \frac{q<em>1 q</em>2}{r^2}

Electric Field

  • Electric field is the modification of space by a charged object.
  • The electric field can be measured using a test charge.

Electric Force Produced by an Electric Field

  • The force on a positive test charge points in the direction of the electric field.
  • The force on a negative test charge points opposite to the electric field.

Electric Field of a Point Charge

  • A point charge qq produces an electric field at all points in space.
  • The field strength decreases with increasing distance.
  • Electric field equation using a unit vector: E⃗=14πϵ0qr2r^\vec{E} = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2} \hat{r}
  • The field produced by a positive point charge points away from the charge.
  • The field produced by a negative point charge points toward the charge.

Superposition of Electric Fields

  • The total electric field at a point is the vector sum of the fields due to all the charges present.

Electric Field Lines

  • An electric field line is an imaginary line or curve whose tangent at any point is the direction of the electric field vector at that point.
  • Electric field lines show the direction of the electric field at each point.
  • The spacing of field lines indicates the magnitude of the electric field.
  • Field lines point away from positive charges and toward negative charges.
  • Field lines never intersect.

Electric Dipole

  • A dipole is formed when there is a displacement of charge.

Water Molecule as an Electric Dipole

  • Water molecules are electrically neutral but have a displacement of charge, creating an electric dipole.
  • The oxygen end has a net negative charge, and the hydrogen end has a net positive charge.
  • Water's dipole nature makes it a good solvent.

Force and Torque on a Dipole

  • In a uniform electric field, the net force on a dipole is always zero, but there can be a net torque.