Electrostatics Vocabulary

Electrostatics: Complete Lessons Guide

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.

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.

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.

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.

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).

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.

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.

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}