Electrostatics Lecture Notes

Introduction to Electrostatics

• Study of charges and their properties.
• Electrostatic refers to charges at rest.

Basic Properties of Charges

1. Types of Charges:
   • Positive
   • Negative
2. Charge Conservation:
   • Total charge in the universe remains constant; charge can only shift from one body to another.
3. Charge Quantization:
   • Charge on a body is quantized as n times e (e = 1.6 x 10^-19 C).
4. Additivity Property:
   • Qnet = Sum of positive and negative charges (with sign).

Charging Methods

• Rubbing (Friction): Example: Rubbing glass with silk cloth causes charge transfer.
• Touching: Charge can be transferred by direct contact.
• Induction:
  • Example: Bringing a charged object near a neutral conductor induces charge separation.
• Earthing: To discharge excess charges.

Electroscope

• Definition: Instrument used to measure charge.
• Working Principle:
  • Metal rod connected to gold leaves; when a charged body touches the rod, leaves diverge.
  • Divergence angle indicates charge magnitude.

Coulomb's Law

• Describes the force between two point charges.
• Formula:
  F = (1 / (4πε₀)) * (Q1 * Q2) / r²
  • ε₀ = Permittivity of free space (8.85 x 10^-12 C²/(N·m²)).
  • K (Coulomb's constant) = 9 x 10^9 N·m²/C².
• Force Characteristics:
  • Attractive if charges are unlike; repulsive if charges are alike.

Modifications in Different Media

• In a medium, replace ε₀ with ε₀ × εᵣ (relative permittivity).
• Dielectric Constant: K = ε₀ × εᵣ.

Vector Form and Additional Examples

• Vector Form of Force:
  F = (1 / (4πε₀)) * (Q1 * Q2) / |R2 - R1|²
• Example Problem: Charge on a square's corners and charge at the center for equilibrium.

Surface Tension and Electrostatics

• Balancing forces due to surface tension and electrostatic forces.
• Force due to Surface Tension: F = 2S * L, where S is surface tension and L is length.
• Example: If four +Q charges are placed on corners of a square, calculate the net force.*

Minimum Velocity for Circular Motion

• For a pendulum with a charge in a circle:
  KQ² / L² is compared with mg for conditions of motion.
  • KQ² / L² > mg (sufficient velocity)
  • KQ² / L² < mg (insufficient velocity)

Conclusion

• Electrostatics covers a range of fundamental principles and laws.
• Focus on Coulomb's law and its applications in various scenarios.
• Further discussion on formulas and important concepts in upcoming lectures.