Electrostatic Potential and Capacitance

Vocabulary flashcards covering key concepts of electrostatic potential, field, equipotentials, dipoles, conductors, grounding, and basic spherical charge distributions as presented in the notes.

Electric Potential (V)

Work done per unit positive charge in bringing a test charge from infinity to a point; reference value V∞ is taken as 0.

Potential Energy (PE or U)

Energy due to the configuration of charges; for a test charge q, PE = qV; also the negative of the work done by conservative forces to assemble the configuration.

Work by External Agent (Wext)

Work done by an external agent to move a charge slowly from infinity to a point against the electric field.

Work by Conservative Force (Wcons)

Work done by electrostatic forces during movement; equals the negative change in potential energy (Wcons = −ΔPE).

Reference Point for Potential

Chosen zero of potential, commonly taken at infinity (PE or V = 0 at ∞).

Interaction Energy

Energy arising from the interaction between charges; another term for the system’s potential energy.

Quasi-Static (Slow) Process

A process carried out slowly enough to keep the system near equilibrium, making Wext ≈ ΔPE.

Electric Potential (V) vs Potential Energy (PE)

V is the potential (voltage); PE is the energy associated with a configuration. PE = qV for a test charge q.

Equipotential Surface

A surface with all points having the same electric potential; electric field is everywhere perpendicular to these surfaces.

Electric Field (E)

Force per unit positive charge; E = F/q; E = −∇V; points in direction of decreasing potential.

Relation E and V along a Path

dV = −E · dr; the line integral of E gives the negative change in potential.

Conductor (Electrostatics)

A material with free charges; in electrostatic equilibrium E inside is zero; charges reside on surfaces; cavities cause surface charges; sharp edges concentrate charge.

Surface Charge Density (σ)

Charge per unit area on a conductor’s surface; higher curvature concentrates charge; outside E ≈ σ/ε0.

Grounding (Earth)

Connecting a body to earth so its potential becomes zero; earth can supply or absorb charge to enforce V = 0.

Dipole Moment (P)

Vector quantity P = Σ qi ri; for a simple dipole of ±q separated by distance d, P ≈ qd; monopole (total charge) is zero for a pure dipole.

Electric Dipole

Two equal and opposite charges separated by a small distance; creates a dipole moment pointing from negative to positive charge.

Electric Field of a Dipole

E at point r due to dipole P: E = (1/4πϵ0)[(3(P·r̂)r̂ − P)/r^3]; along the axis, E ≈ (2P cosθ)/(4πϵ0 r^3).

Dipole in External Field (Energy and Torque)

In a uniform external field, U = −P·E; torque τ = P×E; work to rotate between angles is W = P E (cosθ1 − cosθ2).

Axial vs Equatorial Lines (Dipole)

Axial line is along the dipole moment; equatorial line is perpendicular to the dipole axis.

Torque on a Dipole

τ = P × E; maximum torque occurs at 90° between P and E; stable alignment at θ = 0, unstable at θ = π.

Electric Field Inside a Conductor

In electrostatic equilibrium, E inside a conductor is zero.

Charge Distribution on Conductors

All net charge resides on the outer surface; in cavities, charge resides on the inner surface boundary; sharp points collect more charge (σ is higher at high curvature).

Capacitance (C)

C = Q/V, the ability of a system to store charge per unit potential difference; units are farads.

Potential Outside a Conducting Sphere

For a conducting sphere of radius R and charge Q: V(r) = kQ/r for r > R; inside (r < R) V = kQ/R (constant on the surface and inside).

Potential Inside a Solid Non-Conducting Sphere (Uniform Charge)

For r ≤ R: V(r) = kQ/(2R)[3 − (r^2/R^2)]; for r ≥ R: V(r) = kQ/r.

Potential due to a Charge Distribution

V = ∫(k dq / r); the superposition of contributions from all charges.

Reference for Potentials Relative to Infinity

Using ∞ as the reference point where V = 0 and calculating differences via Vf − Vi.