Fundamentals of Electrostatics: Charge, Fields, and Potential

Electrostatics: Electricity at Rest

Electrostatics is the study of electric charges at rest.

Benjamin Franklin was the first to assign the names positive and negative to the two types of electric charge, noting that the assignment could have been the opposite.

Protons have approximately 1800 times more mass than electrons, but carry the same magnitude of charge.

Quantization of Electric Charge

Electric charge is always quantized. It is formed by small, indivisible packets. The elementary charge is $1.6 \times 10^{-19}$ Coulomb. Charge cannot be less than this value, nor can it be a fractional amount of this elementary charge; only integer multiples are possible.

Coulomb's Law

Coulomb's Law describes the force ($F$) between two point charges:

• $F = K \cdot \frac{q_1 \cdot q_2}{r^2}$

Where $K$ is the proportionality constant, $q_1$ and $q_2$ are the charges of the particles, and $r$ is the distance between them squared.

Types of Materials in Electrostatics

Conductors

Materials containing free electrons that can move throughout the material, allowing charge to flow easily.

Insulators

Materials where electrons are tightly bound to the nucleus and cannot move freely.

Semiconductors

Materials whose conductivity lies between that of conductors and insulators. Their properties can be drastically altered by changing their composition (doping), allowing them to switch between acting as insulators or conductors.

Superconductors

Materials that, when cooled below a critical temperature, exhibit zero electrical resistance and infinite conductivity. Using these materials prevents energy loss due to resistance.

Methods for Charging an Object

Objects can be charged through friction, contact, or induction:

• Friction

  When two neutral materials are rubbed together, electrons are transferred, resulting in one material becoming positively charged and the other negatively charged.

• Contact

  When a charged object touches a neutral object, both objects end up charged with the same sign. The total charge is shared between them.

• Induction

  This method requires a conductive body and results in a charge of the opposite sign to the approaching body. The process involves:

  1. A charged body is brought near a neutral conductor, causing the charges in the conductor to become polarized.
  2. The conductor is connected to the ground (grounded), allowing electrons to flow.
  3. The ground connection is removed while the charged body remains nearby.
  4. The initial charged body is moved away. The conductor is now charged with the opposite sign to the initial approaching charge.

Polarization

The reordering of charges within a neutral material (often an insulator) when brought near a charged object, causing a separation of positive and negative charge centers.

Electric Field and Potential

Electric Field Definition

The electric field ($E$) is defined as the force ($F$) per unit charge ($q$): $E = F/q$.

Electric Shielding (Faraday Cage Effect)

The electric field inside a static metal conductor is always zero. Any external electric field causes the free charges within the conductor to redistribute themselves instantly until the internal field generated by these redistributed charges exactly cancels the external field at every point inside the conductor.

Electric Potential

Electric potential ($V$) is defined as the electrical potential energy per unit charge:

• $V = \frac{\text{Potential Energy}}{\text{Charge}}$
• Units: Volt (V) = Joule (J) / Coulomb (C)

Example: If a point has an electric potential of 120 volts, it means 120 Joules of energy are required per Coulomb of charge moved to that point. This ratio defines the potential; for instance, 240 Joules divided by 2 Coulombs also results in 120 Volts.