Electrostatic Potential and Capacitance Review Flashcards

This set of vocabulary flashcards summarizes key terms, physical laws, and formulas related to electrostatic potential, potential energy, behaviors of conductors and dielectrics, and the operation of capacitors as discussed in the lecture notes.

Conservative Forces

Forces, such as gravitational force, spring force, and Coulomb force, where the work done on an object depends only on its initial and final positions and is stored as potential energy.

Electrostatic Potential Energy ($U$)

The work required to be done by an external force in moving a charge $q$ from one point to another without acceleration against an electrostatic field.

Electrostatic Potential ($V$)

The work done per unit positive test charge in bringing it from infinity to a specific point in an electric field without acceleration.

Electron Volt ($eV$)

A unit of energy equal to the energy gained by an electron when accelerated through a potential difference of $1$ volt, equivalent to $1.6 \times 10^{-19}\,J$.

Potential Due to a Point Charge

The potential at a distance $r$ from a charge $Q$ in a vacuum, mathematically expressed as $V(r) = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$.

Superposition Principle (Potential)

The total electrostatic potential at a point due to a system of charges, which is the algebraic sum of the potentials due to individual charges.

Equipotential Surface

A surface where the electrostatic potential has a constant value at all points, always oriented normal to the electric field at every point.

Electrostatic Shielding

The phenomenon where the electric field inside a cavity within a conductor remains zero regardless of external fields or charges on the conductor's outer surface.

Dielectrics

Non-conducting substances that lack free charge carriers and instead develop induced dipole moments when placed in an external electric field.

Polarisation ($P$)

The dipole moment per unit volume of a dielectric material, which for linear isotropic dielectrics is proportional to the electric field as $P = \chi_e E$.

Capacitance ($C$)

A measure of the ability of a system of conductors to store charge, defined as the ratio of the charge $Q$ to the potential difference $V$ ($C = \frac{Q}{V}$).

Farad ($F$)

The SI unit of capacitance, where $1\,F = 1\,C\,V^{-1}$. Common sub-multiples include $\mu F$, $nF$, and $pF$.

Dielectric Strength

The maximum electric field that a dielectric material can withstand before its insulating properties break down and it begins to conduct electricity.

Parallel Plate Capacitor

A capacitor consisting of two large plane parallel conducting plates of area $A$ separated by a distance $d$, with vacuum capacitance given by $C_0 = \frac{\epsilon_0 A}{d}$.

Dielectric Constant ($K$)

The factor by which the capacitance of a capacitor increases when the space between its plates is fully filled with a specific dielectric material ($K = \frac{C}{C_0}$).

Series Combination of Capacitors

An arrangement where multiple capacitors are connected end-to-end such that the reciprocal of the total capacitance is the sum of the reciprocals of individual capacitances: $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + ...$.

Parallel Combination of Capacitors

An arrangement where capacitors are connected across the same potential difference, resulting in an effective capacitance equal to the sum of individual capacitances: $C = C_1 + C_2 + ...$.

Energy Stored in a Capacitor ($U$)

Total work done in charging a capacitor, expressed as $U = \frac{1}{2} QV = \frac{1}{2} CV^2 = \frac{Q^2}{2C}$.

Energy Density ($u$)

The electrostatic energy stored per unit volume in a region with an electric field, given by $u = \frac{1}{2} \epsilon_0 E^2$.