Overview
This lecture covers Coulomb’s Law, the nature of electric charge in atoms, and step-by-step solutions to typical electric force problems using point charges.
Structure of the Atom & Electric Charge
- Atoms consist of a nucleus (protons and neutrons) and orbiting electrons.
- Protons carry a positive charge (+1.6 × 10⁻¹⁹ C), electrons a negative charge (−1.6 × 10⁻¹⁹ C), neutrons are neutral.
- Charge is quantized: it exists as exact multiples of the elementary charge.
- Objects are neutral if protons = electrons, positive if more protons, negative if more electrons.
Coulomb’s Law & Electric Force
- Opposite charges attract; like charges repel.
- The electric force ( F ) between two point charges is:
( F = k \frac{|q_1 q_2|}{r^2} )
- ( k = 9 \times 10^9 ) N·m²/C²; also ( k = 1/(4\pi \epsilon_0) ), where ( \epsilon_0 = 8.85 \times 10^{-12} ) C²/(N·m²).
- Force doubles if one charge doubles; force becomes one-fourth if distance is doubled (inverse square law).
Units & Conversions
- Charge (q): Coulombs (C); often microCoulombs (μC = 10⁻⁶ C), nanoCoulombs (nC = 10⁻⁹ C), etc.
- Distance (r): meters (m); convert cm to m by dividing by 100.
Example Problems
- For two charges (+10 μC, −20 μC) 25 cm apart:
( F = 28.8 ) N (attraction).
- For charges (800 nC, 900 nC) with ( F = 15 ) N, distance ( r = 2.078 ) cm.
- Two identical charges, 40 cm apart, ( F = 500 ) N: each charge ( q = 94.28 ) μC.
- Number of electrons for −70 μC: ( 4.375 \times 10^{14} ) electrons.
- Charge of ( 5 \times 10^{14} ) protons: +80 μC.
- Net charge on a sphere with ( 4.3 \times 10^{21} ) protons and ( 6.8 \times 10^{21} ) electrons: −400 C (more electrons).
- Net force on charges using vector addition:
- At the origin (100 μC): net force = 22.5 N.
- On 200 μC charge: net force = −8.75 N (negative x-direction).
Key Terms & Definitions
- Coulomb (C) — SI unit of electric charge.
- Point Charge — An idealized charge with negligible size.
- Coulomb’s Law — Law quantifying electric force between point charges.
- Elementary Charge (e) — Smallest unit of electric charge, ( 1.6 \times 10^{-19} ) C.
- Permittivity of Free Space (( \epsilon_0 )) — A constant ( 8.85 \times 10^{-12} ) C²/(N·m²).
Action Items / Next Steps
- Practice converting between units (μC, nC, C) and distances (cm, m).
- Solve additional Coulomb’s Law problems for mastery.
- Review definitions and be able to apply formulas to new problems.