Lecture Notes: Coulomb's Law and Related Concepts

Introduction to the Atom

• At the center of an atom is the nucleus containing:
  • Protons: Positive charge
  • Neutrons: Neutral charge
  • Electrons: Negative charges orbiting the nucleus
  • Charge of a proton: (1.6 \times 10^{-19}) coulombs
  • Charge of an electron: (-1.6 \times 10^{-19}) coulombs
• Quantization of Charge: Charge exists in discrete amounts, always a multiple of fundamental charge

Coulomb's Law

• Describes the electric force between two point charges
• Formula: (F = k \frac{{|q_1 q_2|}}{{r^2}})
  • (k): Proportionality constant (9 \times 10^9 \text{N m}^2/ ext{C}^2)
  • (r): Distance between charges
• Opposite charges attract; like charges repel
• Force magnitude is equal but direction is opposite

Proportionality Constant and Permittivity

• (k = \frac{1}{{4\pi \varepsilon_0}})
  • (\varepsilon_0): Permittivity of free space (8.85 \times 10^{-12} , \text{C}^2/ ext{N m}^2)

Effects of Charge and Distance on Force

• Increasing charge magnitude increases force
• Doubling distance decreases force by a factor of four
• Electric force strongest when charges are closer

Units in Coulomb's Law

• Force (F): Newton (N)
• Charge ((q_1, q_2)): Coulombs (C), often in microcoulombs ((1 , \mu\text{C} = 10^{-6} , \text{C}))
• Distance (r): Meters (m)

Problem Solving with Coulomb's Law

1. Example 1: Calculate force between point charges

   • Charges: (10 , \mu\text{C}, -20 , \mu\text{C})
   • Distance: 25 cm (converted to meters)
   • Result: 28.8 N

2. Example 2: Find distance with given forces and charges

   • Charges: 800 nC, 900 nC
   • Force: 15 N
   • Result: 2.078 cm

3. Example 3: Identical point charges and force calculation

   • Force: 500 N
   • Distance: 40 cm
   • Result: 94.28 (\mu\text{C})

4. Example 4: Convert charge to number of electrons

   • Charge: -70 (\mu\text{C})
   • Result: (4.375 \times 10^{14}) electrons

5. Example 5: Convert protons to electric charge

   • Protons: (5 \times 10^{14})
   • Charge: 80 (\mu\text{C})

6. Example 6: Net electric charge on a sphere

   • Protons: (4.3 \times 10^{21})
   • Electrons: (6.8 \times 10^{21})
   • Result: -400 C (net charge)

Practice Problems

• Example Practice: Net electric force on a charge
  • Analyze forces between charges placed at specific distances
  • Calculate net forces using vector addition and principles of attraction/repulsion

Conclusion

• Understanding the interaction between charged particles is crucial in physics.
• Mastery in calculations and unit conversions is essential for solving problems related to Coulomb's Law.