Overview
This lecture covers Coulomb's Law, the quantization of electric charge, and problem-solving techniques for calculating electric forces between point charges.
Atomic Structure and Electric Charge
- Atoms consist of a nucleus (protons and neutrons) surrounded by electrons.
- Protons have a positive charge; electrons are negative; neutrons are neutral.
- The elementary charge is (1.6 \times 10^{-19}) coulombs, with charge always in integer multiples (quantized).
- Electrons have the same magnitude of charge as protons, but negative.
Coulomb's Law and Electric Force
- Opposite charges attract; like charges repel, with equal and opposite force magnitudes.
- Coulomb’s Law: ( F = k \frac{|q_1q_2|}{r^2} )
- The constant ( k = 9 \times 10^{9} ) N·m²/C²; ( k = 1/(4\pi\varepsilon_0) ) where (\varepsilon_0 = 8.85 \times 10^{-12}) C²/N·m².
- The force increases with larger charges and decreases with greater distance (inverse square law).
Units and Conversions
- Charge (Q) unit: coulombs (C); common multiples: micro- ((10^{-6})), milli- ((10^{-3})), nano- ((10^{-9})).
- Distance (r) should be in meters; convert from centimeters or millimeters as needed.
Example Problems and Solutions
- To find force: substitute charge values (in C) and distance (in m) into Coulomb's Law.
- If either charge doubles, force doubles; if distance doubles, force becomes one-fourth.
- When finding unknown distance or charge, rearrange Coulomb’s Law to solve for the needed variable.
- Converting charge to number of electrons: ( n = Q/e ).
- Converting number of protons/electrons to charge: ( Q = n \times e ).
- Net charge of an object: more protons than electrons = positive charge; more electrons = negative charge.
Multiple Charges: Net Electric Force
- For more than two charges, determine direction and magnitude of forces from each charge.
- Add forces algebraically, considering direction, to find the net force.
- Use absolute values for force magnitudes; direction determined by charge signs and positions.
Key Terms & Definitions
- Coulomb (C) — SI unit of electric charge.
- Elementary charge (e) — (1.6 \times 10^{-19}) C, charge of one proton or electron (negative for electron).
- Coulomb’s Law — Describes magnitude of electric force between two point charges.
- Permittivity of free space ((\varepsilon_0)) — (8.85 \times 10^{-12}) C²/N·m², a physical constant.
Action Items / Next Steps
- Practice converting between units (microcoulombs, nanocoulombs, centimeters, meters).
- Solve additional Coulomb’s Law problems, especially those with multiple charges.
- Review definitions of key constants and ensure familiarity with formula rearrangement.