Electrostatic Potential and Capacitance – Lecture Review

A comprehensive set of Question-and-Answer flashcards covering conservative forces, potential and potential energy, point charges and dipoles, equipotential surfaces, conductor properties, dielectrics, capacitors (construction, combinations, energy), and related formulas and concepts from the lecture transcript.

What defines a conservative force in electrostatics?

A force for which the work done in moving a charge between two points depends only on the initial and final positions, not the path taken (e.g., Coulomb force).

Write the expression for work done by an external force in moving charge q from R to P in an electrostatic field.

WRP = –∫R^P FE·dr = –q∫_R^P E·dr

How is electrostatic potential energy difference (ΔU) between two points R and P defined?

ΔU = UP – UR = work done by external force in moving charge q from R to P without acceleration.

What is the electrostatic potential (V) at a point?

Work done per unit positive test charge in bringing it from infinity to that point: V = W_ext/q.

Give the formula for potential at distance r from a point charge Q.

V(r) = (1/4πϵ0)·Q/r

How does the potential vary with distance r for a point charge?

V ∝ 1/r (inverse–linear).

State the expression for electric potential due to an ideal dipole at a distant point.

V(r) = (1/4πϵ0)·(p·r̂)/r² (for r ≫ dipole size).

On which two factors does the dipole potential depend?

Magnitude of r and angle between dipole moment p and position vector r.

How does dipole potential fall off with distance compared to a single charge?

As 1/r² (dipole) versus 1/r (point charge).

Explain superposition principle for potentials.

Total potential at a point equals algebraic sum of potentials due to individual charges: V = Σ (1/4πϵ0)·qi/ri.

What shape are equipotential surfaces for a single point charge?

Concentric spherical surfaces centred on the charge.

What is always true about the orientation of electric field with respect to an equipotential surface?

E is perpendicular (normal) to every equipotential surface.

Relate magnitude of electric field to potential gradient.

|E| = –dV/dl (rate of fall of potential per unit normal distance).

Write potential energy of a system of two charges q1 and q2 separated by r12.

U = (1/4πϵ0)·q1q2/r12

What is the potential energy of a dipole (p) in a uniform electric field E?

U = –p·E

Define 1 electron-volt (eV).

Energy gained by an electron when accelerated through 1 volt; 1 eV = 1.6×10⁻¹⁹ J.

State any two key electrostatic properties of a conductor in equilibrium.

(i) Electric field inside is zero. (ii) Excess charge resides only on its surface.

Give the formula for electric field just outside a charged conductor’s surface.

E = σ/ϵ0 · n̂ (normal outward).

What is electrostatic shielding?

The interior of a closed conductor remains field-free irrespective of external electric fields.

Distinguish polar and non-polar molecules.

Polar molecules have permanent dipole moment; non-polar have coincident centres of charge and no permanent dipole.

Define polarisation vector P.

Dipole moment per unit volume induced (or aligned) in a dielectric: P = ϵ0χ_e E.

What is dielectric constant K?

Ratio ϵ/ϵ0; equals factor by which capacitance increases when dielectric completely fills a capacitor.

Express permittivity of a dielectric.

ϵ = ϵ0 K

Define capacitance of a capacitor.

C = Q/V, the charge required per unit potential difference between its conductors.

Unit and dimensions of capacitance.

Farad (F); dimensions [M⁻¹L⁻²T⁴A²].

Write capacitance of a parallel-plate capacitor with vacuum.

C0 = ϵ0 A / d

How does inserting a dielectric of constant K affect parallel-plate capacitance?

C = K ϵ0 A / d = K C0

State dielectric strength of air approximately.

≈ 3 × 10⁶ V·m⁻¹

Give the series combination formula for two capacitors C1 and C2.

1/C_eq = 1/C1 + 1/C2

Give the parallel combination formula for two capacitors C1 and C2.

C_eq = C1 + C2

Provide general energy stored in a charged capacitor.

U = ½ C V² = ½ QV = Q²/(2C)

What is energy density of an electric field?

u = ½ ϵ0 E² (energy per unit volume).

Explain why potential inside a conductor is constant.

Because E = 0 inside; no work is required to move charge within, so potential difference is zero everywhere inside.

What happens to capacitance if plate separation halves keeping area and medium same?

Capacitance doubles (C ∝ 1/d).

Why is capacitance large desirable in practical capacitors?

To store more charge without exceeding breakdown voltage; V = Q/C so larger C means lower V for same Q.

State condition for maximum safe charge storage.

Electric field between plates must not exceed dielectric strength of the medium.

What is meant by fringe field in a parallel-plate capacitor?

The bending of electric field lines near the edges causing non-uniformity.

How does induced surface charge density σ_p in a dielectric relate to polarisation?

σ_p = P·n̂ (normal component of P).

Express potential difference across plates with dielectric in terms of free charge density σ.

V = σ d /(ϵ0 K)

Give relation between susceptibility χ_e and dielectric constant K.

K = 1 + χ_e (for linear isotropic dielectrics).

When a charged capacitor is disconnected then filled with dielectric, what stays constant?

Free charge Q on the plates.

When a charged capacitor remains connected to a battery and dielectric is inserted, what stays constant?

Potential difference V across the plates.

Why is work required to rotate a dipole in a uniform field?

Because torque p×E must be opposed; work equals ΔU = pE (cosθfinal – cosθinitial).

What happens to total energy when two identical capacitors (one charged, one uncharged) are connected?

Energy decreases; some energy dissipates as heat/radiation during charge redistribution.

How does electrostatic force stay conservative if charges are fixed in conductors?

External (non-electrostatic) forces hold charges stationary; electrostatic work still path-independent.

Why can charges placed inside a cavity influence outside field despite shielding in reverse?

Shielding only prevents external fields from entering cavity; fields from inside charges terminate on inner walls and affect charge distribution on outer surface, altering external field.