Electrostatics, Electrostatic Potential, Energy, Dipoles, and Conductors

Vocabulary flashcards reviewing core electrostatics concepts including fields, potentials, potential energy, Gauss's law, Poisson and Laplace equations, dipoles, conductors, and capacitors.

Electrostatics

The branch of physics that studies interactions between motionless, electrically charged bodies within a chosen reference frame.

Electric Charge

A fundamental property of matter involved in electromagnetic phenomena, measured in Coulombs ($C$). The elementary charges are $-1.6 \times 10^{-19}\,C$ for an electron and $+1.6 \times 10^{-19}\,C$ for a proton.

Electrization

The phenomenon of charge transfer that causes electric charges to appear on a material, enabling materials to exert attractive or repulsive forces on each other.

Coulomb's Law

The fundamental law stating that the electrostatic force between two point charges $q_A$ and $q_B$ separated by distance $r$ in a vacuum is given by $\vec{F}_{A \rightarrow B} = \frac{1}{4\pi\varepsilon_0} \frac{q_A q_B}{r^2} \vec{u}_{AB}$.

Permittivity of Free Space ($\varepsilon_0$)

The absolute permittivity of a vacuum, equal to $\varepsilon_0 = 8.854 \times 10^{-12}\,F/m$ (or $S.I.$), with the constant $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,N\,m^2\,C^{-2}$.

Relative Permittivity ($\varepsilon_r$)

The dimensionless ratio defining the absolute permittivity of a medium relative to vacuum ($\varepsilon = \varepsilon_0 \varepsilon_r$), with values such as $1.0006$ for air, $80$ for water, $22$ for ammonia, and $2.1$ for paraffin.

Electric Field ($\vec{E}$)

A vector field defined as force per unit charge created by a charge $q_0$ at point $M$ as $\vec{E}_0(M) = \frac{q_0}{4\pi\varepsilon_0 r^2} \vec{u}_r$, measured in volts per meter ($V\,m^{-1}$) or newtons per coulomb ($N\,C^{-1}$).

Principle of Superposition (Electrostatics)

The principle stating that the total electric field created by $N$ discrete charges is the vector sum of individual electric fields: $\vec{E}_{tot} = \sum_{i=1}^N \vec{E}_i = \sum_{i=1}^N \frac{q_i}{4\pi\varepsilon_0 r_i^2} \vec{u}_i$.

Electric Field Lines

Curves in space that are tangent at every point to the local electric field vector, oriented away from positive charges (where they diverge) and toward negative charges (where they converge), and which never intersect.

Volume Charge Density ($\rho$)

The electric charge per unit volume, defining elementary charge $dq = \rho\,dv$ and creating an elementary field integrated over volume $V$ as $\vec{E}_M = \frac{1}{4\pi\varepsilon_0} \iiint_V \frac{\rho\,dv}{r^2} \vec{u}$.

Surface Charge Density ($\sigma$)

The electric charge per unit surface area, defining elementary charge $dq = \sigma\,dS$ and creating an elementary field integrated over surface $S$ as $\vec{E}_M = \frac{1}{4\pi\varepsilon_0} \iint_S \frac{\sigma\,dS}{r^2} \vec{u}$.

Line Charge Density ($\lambda$)

The electric charge per unit length, defining elementary charge $dq = \lambda\,dl$ and creating an elementary field integrated over contour $C$ as $\vec{E}_M = \frac{1}{4\pi\varepsilon_0} \int_C \frac{\lambda\,dl}{r^2} \vec{u}$.

Electrostatic Potential ($V$)

A scalar quantity measured in volts ($V$) whose gradient determines the electric field via $\vec{E}(M) = -\vec{\text{grad}}\,V(M)$, with the electric field vector always pointing toward decreasing potential.

Work of Electrostatic Force

The path integral of electrostatic force $W_{a \rightarrow b} = \int_a^b \vec{F} \cdot d\vec{\ell} = -\Delta U$, where $U$ is potential energy and mechanical energy $K_a + U_a = K_b + U_b$ is conserved.

Electrostatic Potential Energy of a System of Point Charges

The total potential energy stored in an assembly of $n$ point charges, given by $E_p = \frac{1}{2} \sum_{i=1}^n q_i V_i$, where $V_i$ is the potential produced by all other $n-1$ charges at the location of charge $q_i$.

Gauss's Law (Integral Form)

The law stating that the total electric field flux leaving a closed surface $\Sigma$ in vacuum equals the enclosed charge divided by $\varepsilon_0$: $\Phi = \oiint_\Sigma \vec{E} \cdot d\vec{S} = \frac{Q_{int}}{\varepsilon_0}$.

Gauss's Law (Local Form)

The differential formulation of Gauss's law obtained using Ostrogradsky's theorem, expressed as $\text{div}\,\vec{E} = \frac{\rho}{\varepsilon_0}$.

Poisson's Equation

The second-order differential equation relating electrostatic potential $V$ to volume charge density $\rho$, expressed using the Laplacian operator as $\Delta V = -\frac{\rho}{\varepsilon_0}$.

Laplace's Equation

The partial differential equation $\Delta V = 0$, which holds in regions free of electrical charges ($\rho = 0$), showing that electrostatic potential has no local extrema outside charge locations.

Electrostatic Dipole

A system composed of two equal and opposite point charges $+q$ and $-q$ separated by a tiny distance $d$ that is small compared to the observation distance.

Electric Dipole Moment ($\vec{p}$)

A vector defined as $\vec{p} = q\,\vec{AB}$ directed from the negative charge $-q$ to the positive charge $+q$, measured in Debye ($D$), where $1\,D = \frac{10^{-29}}{3}\,C\,m \approx 3.33 \times 10^{-30}\,C\,m$.

Dipole Electrostatic Potential ($V(M)$)

The potential created at a distant point $M$ by an electrostatic dipole: $V(M) = \frac{1}{4\pi\varepsilon_0} \frac{p \cos(\theta)}{r^2} = \frac{1}{4\pi\varepsilon_0} \frac{\vec{p} \cdot \vec{r}}{r^3}$.

Torque on a Dipole in a Uniform Field

The torque acting on a rigid dipole in a uniform electric field $\vec{E}$, given by $\vec{\Gamma}_O = \vec{p} \times \vec{E}$, which tends to rotate and align the dipole moment parallel to the electric field.

Dipole Equilibrium Positions

The orientation states of a dipole in a uniform field: stable equilibrium when aligned (angle $\alpha = 0$) and unstable equilibrium when anti-aligned (angle $\alpha = \pi$).

Dipole Potential Energy in an External Field

The potential energy of a rigid dipole in an external electric field $\vec{E}$, expressed as $E_p = -\vec{p} \cdot \vec{E} = -p E \cos(\alpha)$.

Conductor in Electrostatic Equilibrium

A conductor state with zero motion of mobile charges, resulting in zero internal electric field ($\vec{E}_{int} = \vec{0}$), constant potential throughout its volume (equipotential volume), and excess charges residing entirely on its surface.

Faraday Cage

A hollow conductor or metallic shield whose interior cavity experiences zero electric field ($\vec{E} = \vec{0}$), shielding the interior space from external electric fields.

Coulomb's Theorem (Conductors)

The theorem stating that the electric field immediately outside a charged conductor surface is normal to the surface and has magnitude $\vec{E} = \frac{\sigma}{\varepsilon_0} \vec{n}$.

Self-Capacitance ($C$)

The constant ratio of total charge to electrostatic potential $C = \frac{Q}{V}$ for an isolated conductor, measured in Farads ($F$); for a conducting sphere, $C = 4\pi\varepsilon_0 R$.

Capacitor

A device consisting of two conductors in total electrostatic influence, storing charge according to $Q = C(V_1 - V_2)$, where $C = C_{11} = -C_{21} = -C_{12}$ is its capacitance.

Total Electrostatic Influence

The condition where two conductors are configured such that all field lines originating from one conductor terminate entirely on the other, yielding equal and opposite charges ($Q_2 = -Q_1$).