RS

Electrostatics Vocabulary

Electrostatics: Complete Lessons Guide

Lesson 1: Basics of Electric Charge

  • What is Electric Charge?
    • Fundamental property of matter.
    • Two types: Positive (+) and Negative (-).
    • Like charges repel; opposite charges attract.
  • Charge is Quantized
    • q = n e, where n is an integer.
  • Law of Conservation of Charge
    • Total charge remains constant in an isolated system.
    • Charge is transferred, not created or destroyed.
  • Conductors vs Insulators
    • Conductor:
      • Electrons move freely; charge spreads on the surface.
      • Examples: Metals, human body.
    • Insulator:
      • Electrons are bound; charge stays localized.
      • Examples: Rubber, plastic, glass.
  • Charging Methods
    • Friction: Transfer of charge through rubbing.
    • Conduction: Transfer of charge through direct contact.
    • Induction: Redistribution of charge without direct contact.

Lesson 2: Coulomb's Law

  • Formula:
    • F = k \frac{|q1 q2|}{r^2}, where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
  • k = \frac{1}{4 \pi \epsilon0}, where \epsilon0 is the permittivity of free space.
  • \epsilon_0 = 8.854 \times 10^{-12} C^2/Nm^2
  • k \approx 8.99 \times 10^9 Nm^2/C^2
  • F: magnitude of force.
  • Nature of Force
    • Attractive if charges are opposite.
    • Repulsive if charges are like.
  • Vector Nature
    • Force acts along the line joining the charges.
    • Use vector addition when more than two charges are present.
  • Superposition Principle
    • The net force on a charge is the vector sum of the forces from all other charges.

Lesson 3: Electric Fields

  • Definition:
    • \vec{E} = \frac{\vec{F}}{q}, where \vec{E} is the electric field, \vec{F} is the electric force on a test charge q.
    • Units: N/C or V/m
  • Field from a Point Charge:
    • E = k \frac{|q|}{r^2}
    • Direction: Away from positive charges, toward negative charges.
  • Electric Field Lines
    • Away from positive charges, toward negative charges.
    • More lines indicate a stronger field.
    • Lines never cross.
    • The electric field is tangent to the lines at any point.
  • Superposition of Fields
    • Add vector components to find the net electric field.
  • Common Configurations:
    • Point charge: Electric field radiates spherically.
    • Infinite line: Electric field radiates cylindrically.
    • Infinite plane: Electric field is constant and perpendicular to the plane.
    • Parallel plates: Uniform electric field between the plates.

Lesson 4: Electric Potential

  • What is Electric Potential?
    • Scalar quantity.
    • Work done per unit charge to move a test charge from a reference point to a specific point in the electric field.
    • V = \frac{W}{q}
  • Relation to Electric Field
    • V = - \int \vec{E} \cdot d\vec{l}
  • Equipotential Surfaces
    • Surfaces where the electric potential is constant.
    • Always perpendicular to electric field lines.
    • No work is done moving a charge along an equipotential surface.

Lesson 5: Gauss's Law

  • Statement:
    • \oint \vec{E} \cdot d\vec{A} = \frac{Q{enc}}{\epsilon0}
    • The electric flux through any closed surface is proportional to the enclosed electric charge.
    • Applies to symmetric charge distributions for easy calculation of electric fields.
  • Applications:
    • Spherical symmetry (point charge, sphere).
    • Cylindrical symmetry (infinite wire).
    • Planar symmetry (infinite sheet).

Lesson 6: Conductors in Electrostatics

  • Key Properties:
    • E = 0 inside a conductor in electrostatic equilibrium.
    • Excess charge resides on the surface of a conductor.
    • The surface of a conductor is an equipotential.
    • The electric field just outside a conductor is perpendicular to the surface with magnitude \sigma / \epsilon_0, where \sigma is the surface charge density.
  • Shielding:
    • Conductors block external electric fields.
    • Used in Faraday cages to protect sensitive equipment from external electric fields.

Lesson 7: Capacitors

  • Capacitance:
    • C = \frac{Q}{V}, where C is capacitance, Q is the charge stored, and V is the potential difference.
    • Unit: Farad (F).
  • Parallel Plate Capacitor:
    • C = \epsilon_0 \frac{A}{d}, where A is the plate area and d is the distance between the plates.
  • Energy Stored:
    • U = \frac{1}{2} CV^2 = \frac{1}{2} QV = \frac{1}{2} \frac{Q^2}{C}
  • Dielectrics:
    • Inserting a dielectric increases capacitance.
    • C' = K C, where K is the dielectric constant.

Lesson 8: Electric Dipoles

  • Definition:
    • Two equal and opposite charges (+q and -q) separated by a distance d.
  • Dipole moment:
    • \vec{p} = q \vec{d}, where \vec{p} is the dipole moment vector, pointing from the negative charge to the positive charge.
  • Torque in Electric Field:
    • \vec{\tau} = \vec{p} \times \vec{E}
    • \tau = p E \sin(\theta)
  • Potential Energy:
    • U = - \vec{p} \cdot \vec{E}
    • U = -p E \cos(\theta)
  • Electric Field of a Dipole (approx., far away):
    • Along the axis: E = \frac{2kp}{r^3}
    • Perpendicular to the axis: E = \frac{kp}{r^3}