Lecture Notes: Electrostatic Potential and Capacitance

Introduction

• Greetings and motivation: Success requires hard work, sincerity, and consistency.
• Focus on Physics (Electrostatic Potential and Capacitance), Chemistry (Solutions), and Mathematics.

Key Concepts and Formulas

Electric Flux

• Definition: Electric flux (Φ) is calculated as the dot product of the electric field (E) and the area (A), i.e., Φ = E · A.
• Example Problem: Electric field = 3 × 10³ N/C through a square side 10 cm parallel to the yz-plane:
  • Area vector is along x-axis.
  • Flux = E × A × cos(θ) where θ is the angle between E and A.
  • Flux calculated as 30 Nm²/C.

Charge and Electric Field Relationships

• Coulomb's Law: Electric field (E) due to a point charge (Q) is E = KQ/r².
• Example Problem: Determine the distance for a specific electric field magnitude, solve using E₁ = E₂ for two point charges.

Gauss's Law

• Definition: Net electric flux through a closed surface is equal to the charge enclosed divided by ε₀ (permittivity of free space).
• Example Problems: Calculating net charge based on electric flux through surfaces.

Dipoles and Torque

• Dipole Moment (p): Defined as the product of charge (q) and separation distance (d). p = q × d.
• Torque (τ): τ = p × E × sin(θ), where θ is the angle between p and E.
• Net Dipole Moment: Resultant of two dipoles can be found using vector addition.

Problem-Solving Techniques

• Vector Addition: For calculating resultant electric fields and dipole moments.
• Use of Symmetry: In problems involving equilateral triangles or symmetric charge distributions.

Practice Problems and Solutions

• Electric Fields in Cubes: Analyze electric fields using Gauss's Law and symmetry. Calculate flux through surfaces and net charge enclosed.
• Torque on Dipoles: Use vector cross product to determine torque on dipoles in an electric field.

Closing Remarks

• Emphasis on consistent practice and problem-solving.
• Encouragement to join group discussions and study sessions.

Additional Resources

• Suggestion to take practice exams for self-assessment and preparation.

Conclusion

• Thank participants for their engagement and encourage them to continue studying and practicing.