Electrostatics

The One Thing

Electrostatics describes how electric charges produce forces, electric fields and electric potentials, with multiple-charge systems analysed through superposition and symmetry. Capacitance extends this framework to the storage of charge and electrical energy by separating equal and opposite charges on conductors.

Reactions, Processes and Experiments

Key Terms

• Electric charge: A physical property responsible for electric interaction. Charge may be positive or negative, is conserved, and occurs in integral multiples of the elementary charge.
• Quantisation of charge: The charge on a body is q = ne, where n is an integer and e = 1.6 × 10^-19 C.
• Coulomb's law: The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of their separation.
• Principle of superposition: The net force or electric field due to several charges is the vector sum of the forces or fields produced by the charges individually.
• Electric field: The force experienced by a unit positive test charge placed at a point: E = F/q.
• Electric field lines: Imaginary lines whose tangent gives the direction of the electric field. They begin on positive charges and end on negative charges or infinity, and never intersect.
• Electric dipole: A pair of equal and opposite charges separated by a small distance. Its dipole moment is p = qd, directed from negative to positive charge.
• Electric flux: A measure of the electric field passing through a surface. For a uniform field, flux is Φ = EA cos θ.
• Gauss's law: The total electric flux through a closed surface equals the enclosed charge divided by ε0: ∮E·dA = Qenclosed/ε0.
• Electric potential: The work done per unit positive test charge in bringing it from infinity to a point without acceleration: V = W/q.
• Potential difference: The work done per unit charge in moving a test charge between two points: V_B − V_A = W_AB/q.
• Relation between field and potential: The electric field points in the direction of decreasing potential and is related to potential by E = −dV/dr in one dimension.
• Equipotential surface: A surface on which electric potential is constant. No work is done in moving a charge along it, and electric field lines meet it normally.
• Electrostatic equilibrium: A condition in which charges in a conductor are at rest. The electric field inside the conductor is zero and excess charge resides on its surface.
• Capacitance: The ability of a conductor or capacitor to store charge per unit potential difference: C = Q/V.
• Parallel-plate capacitor: A capacitor made of two large parallel conducting plates separated by an insulating medium. Its capacitance in vacuum is C = ε0A/d.
• Dielectric: An insulating material placed between capacitor plates that becomes polarised and generally increases capacitance.
• Dielectric constant: The relative permittivity of a material, K = ε/ε0. For a completely filled capacitor, C = Kε0A/d.
• Energy stored in a capacitor: The energy stored in charging a capacitor is U = 1/2 CV^2 = 1/2 QV = Q^2/(2C).
• Polarisation: The slight separation or alignment of positive and negative charges within a dielectric placed in an electric field.
• Potential energy: The energy associated with the position or configuration of charges in an electric field.
• Conservative electrostatic force: An electrostatic force for which work is path independent, allowing the definition of electric potential energy.
• Elementary charge: The magnitude of the smallest unit of charge, e = 1.6 × 10^-19 C.
• Dielectric constant K: The relative permittivity of a material, defined by K = ε/ε0.
• Electric field units: N C^-1 or V m^-1.
• Potential unit: Volt (V).
• Capacitance unit: Farad (F).
• Electric flux unit: The flux is measured consistently with the relation Φ = Qenclosed/ε0.
• Dipole moment unit: Coulomb metre (C m).
• Permittivity of free space: ε0 = 8.85 × 10^-12 C^2 N^-1 m^-2.
• Coulomb constant: 1/(4πε0) ≈ 9 × 10^9 N m^2 C^-2.

Easily Confused

• Electric field and electric potential: Electric field is a vector quantity, whereas electric potential is a scalar quantity.
• Electric field and electric flux: Electric field describes force per unit positive charge; electric flux measures the field passing through a surface.
• Potential and potential difference: Potential is defined relative to infinity, whereas potential difference concerns work per unit charge between two points.
• Conductors and dielectrics: A conductor permits charge movement and has zero electric field inside in electrostatic equilibrium; a dielectric is an insulator that becomes polarised in an electric field.
• Capacitors in parallel and series: Parallel capacitors have the same potential difference and capacitances add directly; series capacitors have the same charge magnitude and reciprocals of capacitance add.
• Battery-connected and isolated dielectric insertion: With a battery connected, V remains constant and Q increases by K; when isolated, Q remains constant and V becomes V/K.
• Dipole moment and dipole potential energy: Dipole moment is p = qd and points from negative to positive charge; dipole potential energy is U = −pE cos θ.
• Field of an infinite plane sheet and field just outside a charged conductor: The sheet field is E = σ/(2ε0), whereas the field just outside a charged conductor is E = σ/ε0.
• Electric field and potential energy: Electric field is force per unit charge, whereas potential energy is the energy associated with a charge configuration.

What Gets Asked

• Calculate the force between two point charges using Coulomb's law, including the correct dependence on charge magnitudes and separation: F = (1/(4πε0)) |q1q2|/r^2. A common mark-losing error is treating the force as proportional to 1/r rather than 1/r^2.
• Determine the resultant force or electric field from several charges using the principle of superposition. The key slip is adding vector quantities as ordinary scalars without accounting for direction.
• Derive or apply electric fields for a point charge, an infinite plane sheet of charge, and a charged conductor. The stated expressions must not be interchanged: E = (1/(4πε0)) |q|/r^2, E = σ/(2ε0), and E = σ/ε0 respectively.
• Use Gauss's law or calculate electric flux through a closed surface. The relevant relation is ∮E·dA = Qenclosed/ε0, so the enclosed charge, rather than the total charge outside the surface, determines the net flux.
• Calculate electric potential, potential difference and potential energy. The common distinction required is that potential is scalar and potentials from several point charges add as V = (1/(4πε0)) Σ(qi/ri), whereas electric fields require vector addition.
• Analyse capacitors in series or parallel and determine equivalent capacitance. Parallel combinations use Ceq = C1 + C2 + C3 + ..., while series combinations use 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ...; confusing the two expressions loses marks.
• Determine how inserting a dielectric changes a capacitor. The result depends on whether the capacitor remains connected to a battery: V remains constant when connected, whereas Q remains constant when isolated.