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:
  • $F = k \frac{|q<em>1 q</em>2|}{r^2}$, where $k$ is Coulomb's constant, $q<em>1$ and $q</em>2$ are the magnitudes of the charges, and $r$ is the distance between the charges.
• $k = \frac{1}{4 \pi \epsilon<em>0}$, where $\epsilon</em>0$ 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:
  • $\oint \vec{E} \cdot d\vec{A} = \frac{Q<em>{enc}}{\epsilon</em>0}$
  • 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: $E = \frac{kp}{r^3}$