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Electric Forces and Fields Cheat Sheet

The core ideas of Electric Forces and Fields distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Coulomb's Law

The electrostatic force between two point charges is $F = k |q_1 q_2| / r^2$, where $k = 8.99 \times 10^9$ N m$^2$/C$^2$ is Coulomb's constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. Like charges repel; opposite charges attract.

Electric Field

A vector field that represents the force per unit positive test charge at every point in space: $\vec{E} = \vec{F}/q$. The electric field due to a point charge is $E = kq/r^2$, directed radially outward for positive charges and inward for negative charges.

Electric Field Lines

Imaginary lines used to visualize electric fields. They start on positive charges and end on negative charges (or extend to infinity). The density of lines at a point is proportional to the field strength, and the tangent to a line gives the field direction. Field lines never cross.

Superposition Principle

The net electric field at any point due to multiple charges is the vector sum of the individual fields from each charge. Similarly, the net force on a charge is the vector sum of forces from all other charges. This principle holds because electric fields obey linearity.

Electric Potential

The electric potential $V$ at a point is the electric potential energy per unit positive charge: $V = U/q = kQ/r$ for a point charge. It is a scalar quantity measured in volts (1 V = 1 J/C). Potential differences, not absolute potentials, are physically meaningful.

Electric Potential Energy

The energy stored in a system of charges due to their positions: $U = kq_1q_2/r$ for two point charges. Positive $U$ means repulsion (like charges); negative $U$ means attraction (opposite charges). This energy can be converted to kinetic energy as charges move.

Gauss's Law

The total electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space: $\oint \vec{E} \cdot d\vec{A} = Q_{\text{enc}} / \epsilon_0$. This law is most useful when charge distributions have high symmetry (spherical, cylindrical, or planar).

Conductors in Electrostatic Equilibrium

In a conductor at electrostatic equilibrium: (1) the internal electric field is zero, (2) excess charge resides entirely on the surface, (3) the surface is an equipotential, and (4) the external field is perpendicular to the surface. These properties arise because free charges redistribute until no net force acts on them.

Insulators and Dielectrics

Materials in which charges are not free to move throughout the bulk. When placed in an electric field, the molecules in a dielectric polarize (positive and negative ends shift), reducing the internal field. The dielectric constant $\kappa$ quantifies this reduction: $E_{\text{inside}} = E_0 / \kappa$.

Key Terms at a Glance

Coulomb's Law:The law stating that the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Electric Field:A vector field giving the force per unit positive charge at each point in space. Units: N/C or V/m.
Electric Potential:The electric potential energy per unit charge at a point in space. A scalar quantity measured in volts (V = J/C).
Electric Flux:The surface integral of the electric field over a surface: $\Phi_E = \oint \vec{E} \cdot d\vec{A}$. It measures the 'flow' of field lines through the surface.
Gauss's Law:A fundamental law relating the electric flux through a closed surface to the total charge enclosed: $\Phi_E = Q_{\text{enc}}/\epsilon_0$.
Superposition Principle:The net field or force from multiple charges is the vector sum of the individual contributions from each charge.
Equipotential Surface:A surface on which all points are at the same electric potential. The electric field is always perpendicular to equipotential surfaces.
Conductor:A material with free charges that can move throughout the volume. In electrostatic equilibrium, the internal field is zero and excess charge resides on the surface.
Insulator (Dielectric):A material in which charges are bound and cannot move freely. An external field polarizes the molecules but does not create a current.
Permittivity of Free Space:The constant $\epsilon_0 = 8.85 \times 10^{-12}$ C$^2$/(N m$^2$) that appears in Coulomb's law and Gauss's law. Related to Coulomb's constant by $k = 1/(4\pi\epsilon_0)$.
Electric Dipole:A pair of equal and opposite charges $+q$ and $-q$ separated by a distance $d$. The dipole moment is $p = qd$, pointing from $-q$ to $+q$.
Potential Difference (Voltage):The difference in electric potential between two points: $\Delta V = V_B - V_A$. It equals the work done per unit charge in moving a charge between those points.
Electron-Volt (eV):A unit of energy equal to the work done on an electron accelerated through 1 V of potential difference: $1 \text{ eV} = 1.6 \times 10^{-19}$ J.

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Electric Forces and Fields Cheat Sheet - Quick Reference Guide | PiqCue