Comprehensive Guide to Conductors, Capacitors, and Dielectrics

Conductor

A material containing charge carriers, usually electrons, that are free to move.

Electrostatic Equilibrium

The state reached when all net charge movements in a conductor have ceased.

Electric Field Inside a Conductor

The electric field inside a conductor in electrostatic equilibrium is zero.

Net Charge on Conductors

All excess charge resides on the surface of a conductor.

Electric Field Surface Relation

The electric field is perpendicular to the surface of a conductor.

Equipotential

The entire conductor is an equipotential, meaning potential is constant throughout.

Cavity in Conductor

An empty cavity inside a conductor has no charge and an electric field of zero.

Charge Inside Cavity

A point charge inside a cavity induces an equal but opposite charge on the inner wall.

Capacitance

Capacitance (C) measures how much charge (Q) a system can store per unit potential difference (ΔV).

Unit of Capacitance

The unit of capacitance is the Farad (F), where 1 F = 1 C / 1 V.

Parallel Plate Capacitors Field

The electric field (E) between two parallel plates is given by E = σ/ε₀ = Q/(ε₀A).

Parallel Plate Capacitors Potential

The potential difference (ΔV) is given by ΔV = E · d = Qd/(ε₀A).

Capacitance of Parallel Plates

Capacitance (C) of parallel plates is given by C = ε₀A/d.

Cylindrical Capacitors Field

The electric field (E) in cylindrical capacitors is given by E = λ/(2πε₀r).

Capacitance of Cylindrical Capacitors

Capacitance (C) for cylindrical capacitors is given by C = (2πε₀L)/(ln(b/a)).

Spherical Capacitors Field

The electric field (E) in spherical capacitors acts like a point charge, E = Q/(4πε₀r²).

Capacitance of Spherical Capacitors

Capacitance (C) for spherical capacitors is given by C = 4πε₀(ab/(b-a)).

Equivalent Capacitance in Parallel

For capacitors in parallel, the equivalent capacitance is Ceq = C1 + C_2 + …

Equivalent Capacitance in Series

For capacitors in series, the equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C_2 + …

Energy Stored in Capacitors

The energy stored in a capacitor is given by U_C = (1/2)QV = (1/2)CV².

Energy Density in Electric Field

The energy density (uE) stored in an electric field is uE = (1/2)ε₀E².

Dielectric

A dielectric is an insulating material placed between capacitor plates that increases capacitance.

Dielectric Constant

The dielectric constant (κ) is a factor by which the capacitance increases when a dielectric is inserted.

Polarization Mechanism of Dielectrics

In an external electric field, dipoles in dielectrics align causing an induced field that opposes the external field.

Effect on Capacitance with Dielectric (Disconnected)

With a disconnected battery, inserting a dielectric increases capacitance while keeping charge constant.

Effect on Capacitance with Dielectric (Connected)

With a connected battery, inserting a dielectric increases capacitance and also increases charge.

Electric Field in Dielectrics (Disconnected)

When a dielectric is inserted while disconnected, the electric field inside decreases.

Stored Energy with Dielectric (Disconnected)

Inserting a dielectric when disconnected decreases stored energy.

Potential Difference (Voltage) in Conductors

If the electric field is zero inside a conductor, the potential is constant, not necessarily zero.

Capacitance vs. Resistance Formulas

Capacitors in parallel add directly, while those in series add inversely, opposite to resistors.

Inserting Dielectric Energy Misconception

When a dielectric is inserted into an isolated capacitor, it can decrease stored energy rather than always increasing it.

Charge Distribution in Conductors

Charge is not evenly distributed on irregularly shaped conductors; it accumulates at sharp points.

Gauss's Law

Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed charge.

Surface Charge Density

Surface charge density (σ) is defined as charge per unit area on a conductor's surface.

Uniform Electric Field

A uniform electric field maintains consistent strength and direction across a given area.

Potential Difference Dependency

Potential difference (ΔV) across a capacitor depends on both the capacitance and charge stored.

Static Electric Charge

Static electric charge refers to the stationary electric charge that accumulates on an object.

Charge Conservation Principle

The principle that the total electric charge in an isolated system remains constant.

Induced Charge

Induced charge is the charge that appears on the surface of a conductor due to the influence of an external electric field.

Field Lines in Conductors

Field lines from a charged conductor always begin and end on charge surfaces.

Electrostatic Shielding

Electrostatic shielding is the phenomenon where the electric field inside a conductor is reduced to zero.

Electric Potential Energy

Electric potential energy is the energy stored due to the position of charges within an electric field.

Charge Carriers

Charged particles, typically electrons, that are free to move in conductors.