Electrostatics and Gauss's Law

Division of Chapter

• Part 1: Electrostatics Field and Potential
  • Point charges, system of charges, dipoles
  • Fields, energies, forces, potentials due to these charges
• Part 2: Gauss's Law (separate class)
  • Applications, geometries like shells, sheets, spheres, conductor properties

Introduction to Electrostatics

• Electrostatics deals with forces, fields, and potentials due to charges at rest.
• Electric Force: Attraction or repulsion due to electric charges.
  • Comes from charges: Positive (protons) or Negative (electrons)

Basic Concepts

• Like Charges: Repel each other
• Unlike Charges: Attract each other
• Neutral Bodies: Neither attract nor repel
• Quantization of Charge
  • Charge is found in multiples of the elementary charge (e = 1.6 × 10^-19 C)
• Conservation of Charge
  • Total charge in an isolated system remains constant

Coulomb's Law

• Formula: F = k * (q1 * q2) / r^2
  • k = 9 × 10^9 Nm^2/C^2
• Vector Form: F = k * (q1 * q2) / r^3 * r_vector
• Applications: Calculating forces between point charges

Electric Field (E)

• Definition: E = F / q (Force per unit positive test charge)
  • SI Unit: N/C or V/m
• Point Charge Field: E = kQ / r^2
• Superposition Principle for Electric Fields
  • Net electric field is vector sum of individual fields

Electric Potential (V)

• Definition: Work done to bring a unit positive charge from infinity to a point
  • V = W / q
  • SI Unit: Volt (V) or J/C
  • Potential Difference: V = V2 - V1
• Potential Due to Point Charge: V = kQ / r
• Superposition Principle for Potentials
  • Net potential is algebraic sum of individual potentials

Relationship Between Electric Field and Potential

• Formula: E = -dV/dr (Electric field is negative gradient of potential)
• Equipotential Surfaces
  • Surfaces where potential is constant
  • Electric field lines are perpendicular to equipotential surfaces

Electric Dipoles

• Dipole Moment (p): p = q * d (Charge * separation distance)
  • Unit: C·m, Direction from negative to positive charge
• Field and Potential Due to Dipole
  • On Axis: E = (2k*p) / r^3
  • On Equator: E = (k*p) / r^3
  • Potential: V = (k * p * cosθ) / r^2
• Dipole in External Field
  • Torque (τ): τ = pE sinθ = p ⨯ E
  • Potential Energy (U): U = -p · E

Problems and Examples

• Calculation of forces, fields, potential, and potential energy for various charge configurations
• Applying superposition principle for multiple charges
• Understanding equilibrium positions in uniform and non-uniform fields

Key Takeaways

• Mastery of Coulomb's law and vector addition for forces and fields
• Understanding of basic electrostatic principles: conservation, quantization of charge
• Ability to calculate and understand electric potential and potential energy
• Comprehension of dipole behavior in different fields

Note: For detailed problems and examples, refer to the assigned DPPs and the lecture slides. Ensure practice of a variety of problems to solidify understanding and prepare for exams.