Electrostatic Potential and Capacitance

Flashcards covering the definitions, principles, and mathematical formulas of Electric Potential, Capacitance, and Dielectrics as per the lecture notes.

Electric Potential ($V$)

The amount of work done in moving a unit positive charge from infinity to a point in an electric field against the electrostatic force ($V = \frac{W}{q_0}$).

Potential Difference

The amount of work done in moving a unit positive charge from one point to another in an electric field against the electrostatic force ($V_B - V_A = \frac{W_{BA}}{q_0}$).

Volt ($v$)

The unit of electric potential; it is said to be $1\text{ Volt}$ if $1\text{ Joule}$ of work is done in moving a positive charge of $1\text{ Coulomb}$ from infinity to a point ($1\text{ Volt} = \frac{1\text{ Joule}}{1\text{ Coulomb}}$).

Electric Potential due to a Point Charge

The potential at a point P located at distance 'r' from a charge Q, given by the formula $V = \frac{KQ}{r}$.

Electric Dipole Potential (Axial)

The potential at a point 'P' at distance 'r' from the center of a dipole of length '2a', given by $V = \frac{Kp}{r^2 - a^2}$; for a short dipole where $r \text{ } \text{\textgreater\textgreater} \text{ } a$, $V = \frac{Kp}{r^2}$.

Equatorial Electric Potential of a Dipole

The potential at any point on the equatorial line of an electric dipole is zero because the distances from the positive and negative charges are equal ($V = 0$).

Potential Gradient

The negative rate of change of potential with distance in the direction of the electric field ($E = -\frac{dv}{dr}$), usually expressed in units of $\text{V/m}$; the negative sign indicates potential decreases in the direction of the electric field.

Equipotential Surface

A surface at every point of which the electric potential is the same; work done in moving a charge between two points on this surface is zero.

Electric Potential Energy ($U$)

The total amount of work done in order to move charges from infinity to their respective points in a system; for two charges, $U = \frac{Kq_1q_2}{r_{12}}$.

Electrostatic Shielding

The phenomenon of protecting a region of space from external electric fields by creating a field-free region, often called a Faraday Cage.

Dielectrics

Insulating materials that do not allow electric current to flow through them but allow electric field effects; they only reduce the external electric field rather than making it zero.

Polar Dielectrics

Substances whose molecules have centers of positive and negative charges that do not coincide, resulting in a permanent dipole moment ($p \neq 0$), such as $\text{H}_2\text{O}$.

Non-polar Dielectrics

Substances whose molecules have coinciding centers of positive and negative charges, resulting in no permanent dipole moment ($p = 0$), such as $\text{H}_2$ and $\text{CO}_2$.

Dielectric Constant ($K$)

The ratio of the external electric field ($E_0$) to the net electric field ($E$) inside the dielectric material ($K = \frac{E_0}{E}$).

Polarisation Density ($P$)

A vector quantity defined as the dipole moment per unit volume ($P = \frac{p}{V}$), which is directly proportional to the reduced electric field (P = \text{\textchi}_e \text{\textepsilon}_0 E).

Dielectric Strength

The maximum electric field that a dielectric material can withstand without breaking down and becoming conductive.

Capacitor

An arrangement of two parallel conductive plates separated by an insulating material (dielectric) used for storing large amounts of electric charge and electrical energy.

Capacitance ($C$)

The ability of a capacitor to store electric charge or energy, calculated as the ratio of charge to potential ($C = \frac{Q}{V}$).

Farad ($F$)

The unit of capacitance; a conductor has a capacitance of $1\text{ Farad}$ if adding $1\text{ Coulomb}$ of charge increases its potential by $1\text{ Volt}$.

Capacitance of Earth

Calculated by treating the Earth as an isolated spherical conductor resulting in approximately $0.711 \times 10^{-3}\text{ Farad}$ or 711\text{ \textmu F}.

Energy Stored in a Capacitor ($U$)

The potential energy stored in the electric field between the plates of a capacitor, given by $U = \frac{1}{2} CV^2 = \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} QV$.

Energy Density ($u$)

The energy stored per unit volume of a capacitor, expressed as u = \frac{1}{2} \text{\textepsilon}_0 E^2.

Common Potential ($V$)

The shared potential achieved after the redistribution of charges when two conductors are connected, given by $V = \frac{C_1V_1 + C_2V_2}{C_1 + C_2}$.

Electron Volt ($eV$)

The unit of electrostatic energy defined as the energy gained or lost by an electron moving through a potential difference of $1\text{ Volt}$ ($1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$).