Electric charge and basic properties

Electric charge is a fundamental property of matter associated with electrical interaction. Positive and negative charges attract when opposite and repel when like. In the SI system charge is measured in coulombs (C); the elementary charge magnitude is e≈1.602×10⁻¹⁹ C. Protons carry +e and electrons carry −e, while neutrons are electrically neutral.

Three central properties guide electrostatics: charge is conserved in isolated systems, charge is quantized in integral multiples of e for ordinarily isolated objects, and net charge adds algebraically. Friction or contact charging transfers charge between bodies; it does not produce net electric charge from nothing. Electric charge of macroscopic objects can be huge in numbers of elementary charges despite appearing small in coulombs.

• Charge conservation concerns total charge, not separately fixed electron counts for each body.
• ‘Positive body’ usually means an electron deficit, not an extra amount of protons moved around.

Conductors, insulators, charging and induction

In conductors such as metals, charge carriers can move relatively freely; in insulators such as dry plastic they remain much more tightly bound. Charging by friction or contact involves transfers between objects, while electrostatic induction uses an external charged body to redistribute charges without direct contact. A neutral conductor placed near a positive rod can polarize with more negative charge on the near side and positive charge on the far side.

Grounding provides a conductive pathway for charge to enter or leave a body. A nearby charged object plus grounding can leave the body charged after a suitable sequence of removal of ground and external source. Polarization of a neutral insulator shifts bound charges microscopically and can cause attraction even though total charge remains zero. Always distinguish redistribution from net charge transfer.

• A neutral body can be attracted to a charged rod due to polarization.
• Contact charging and induction use different sequences of electron movement.

Coulomb’s inverse-square law

The electrostatic force between stationary point charges q₁ and q₂ separated by distance r in vacuum has magnitude F=k|q₁q₂|/r², where k=1/(4πε₀)≈8.99×10⁹ N·m²/C². The force acts along the line joining charges and is attractive or repulsive depending on signs. Electrostatic force is central and obeys Newton’s third law for a simple pair of stationary point charges.

Doubling the separation reduces magnitude to one-fourth; doubling either charge doubles force magnitude. In a uniform dielectric medium the effective force is reduced relative to vacuum by the material’s relative permittivity in the usual electrostatic idealization. Do not confuse electric field with force: the field is defined per unit test charge, independent of its chosen magnitude when it does not significantly disturb the source configuration.

• The force law is vectorial; use signs and direction after finding magnitude.
• Coulomb’s formula assumes point charges and a specified medium.

Electric field and superposition

Electric field at a location is the force per unit small positive test charge: E=F/q₀ in the non-disturbing limit. A point source charge Q creates E=k|Q|/r² radially outward for positive Q and inward for negative Q. In vector form fields from different sources add by superposition, E_net=ΣEᵢ.

Superposition is essential in multiple-charge problems. For two identical positive charges symmetrically placed about a midpoint, their fields cancel at that midpoint, though the electric potential there is positive. For two equal and opposite charges, midpoint electric fields point in the same direction and add; potential may cancel to zero. These differences demonstrate why field and potential must be treated separately.

• Electric field units: N/C or V/m.
• A field can be zero at a point while potential is nonzero.

Electric field lines: direction and interpretation

Field lines are visual guides whose tangent indicates electric-field direction and whose relative density indicates field strength in the conventional sketch. Lines conventionally begin on positive charges and end on negative charges or at infinity. For electrostatic fields, field lines do not intersect because a nonzero vector field at a point has a unique direction.

In electrostatic equilibrium, field lines meet a conducting surface normally; a tangential electric field would cause mobile surface charges to move. Field lines are a conceptual visualization, not material strings. Their number in a diagram is arbitrary, so quantitative field strength should be calculated from charges and geometry rather than counting exact drawn lines.

• A negative charge attracts lines inward; positive charge sends them outward.
• Two electrostatic field lines cannot cross in a well-defined field.

Electric dipole, dipole moment and torque

An electric dipole consists of equal and opposite charges separated by displacement vector d from negative to positive charge. Its dipole moment p=q d points from negative toward positive charge and has SI unit C·m. In a uniform external field, the net force on an ideal dipole is zero but the dipole experiences torque τ=p×E, magnitude τ=pE sinθ.

The potential energy of an ideal dipole in a uniform field is U=−p·E, so stable alignment has p parallel to E, corresponding to minimum potential energy. Nonuniform electric fields can exert a net force on a dipole. The dipole’s far field decreases as 1/r³, faster than the 1/r² field from an isolated point charge.

• Dipole moment direction is − to +.
• Uniform field can rotate an ideal dipole without giving a net translational force.

Electric flux and Gauss’s law

Electric flux through a surface is the surface integral Φ_E=∫E·dA. For a uniform field passing through a flat area A at angle θ to the area normal, Φ=EA cosθ. Its SI unit is N·m²/C. Flux measures the oriented amount of electric field passing through a surface; it is not the number of particles crossing a physical net.

Gauss’s law states that total electric flux through any closed surface equals total charge enclosed divided by permittivity of vacuum: ∮E·dA=Q_enclosed/ε₀. Charges outside a closed surface can influence the local field on its surface but contribute zero net closed-surface flux. Zero enclosed charge implies zero net flux, not necessarily zero electric field at every point.

• Only charge enclosed determines total flux through a closed Gaussian surface.
• Gauss’s law is exact electrostatics; using it to compute E easily requires sufficient symmetry.

Spherical, cylindrical and planar charge distributions

Gauss’s law is especially powerful for charge distributions with symmetry. For an infinitely long straight line of uniform charge density λ, a cylindrical Gaussian surface gives E=|λ|/(2πε₀r). For an ideal infinite uniformly charged nonconducting plane with surface density σ, the field magnitude on either side is |σ|/(2ε₀).

For a conducting spherical shell in electrostatic equilibrium, the electric field inside the conducting material is zero; for an isolated charged spherical shell with no charges in its cavity, the electric field within the empty cavity is zero. Outside a spherical uniformly charged shell, E behaves as that of a point charge at its centre. These results require careful distinction between a conductor, insulator and presence of internal charges.

• Line-field magnitude falls as 1/r; infinite-plane field is independent of distance.
• For spherical symmetry, field outside depends on total enclosed charge.

Electrostatic equilibrium inside conductors

A conductor at electrostatic equilibrium has zero electric field within its conducting material, and the conductor’s entire connected body is at a constant electric potential. Any excess net charge resides on exposed surfaces in the ideal classical treatment. If a static internal field existed in the metal, mobile charges would move until it vanished.

Electric shielding is based on charge redistribution: a closed conducting shell can protect interior regions from many static external electric fields, provided the shell and geometry meet appropriate conditions. Sharp surface features can have larger electric fields and promote corona discharge at sufficient field strengths. The field just outside a surface depends on local surface charge density.

• Electrostatic equilibrium means no sustained current from an internal electric field.
• Electric potential can be constant even when its numerical value is not zero.

Electric potential, work and equipotentials

Electric potential V at a point is potential energy per unit positive charge, with unit volt (V=J/C). For a point charge Q taking zero potential at infinity, V=kQ/r. Potential is a scalar and adds algebraically, making multi-charge potential calculation often easier than electric field vector calculation.

The potential difference between points relates to work per unit charge, and electrostatic fields point toward decreasing potential: E=−∇V. Work done by the electric field in moving charge q from A to B is q(V_A−V_B). Along an equipotential surface, electric field does no work for an infinitesimal tangential displacement because potential does not change.

• Electric field is perpendicular to equipotential surfaces wherever it is nonzero.
• A zero potential point does not necessarily have zero electric field.

Capacitance and parallel-plate capacitors

Capacitance measures the charge stored per unit potential difference across a two-terminal capacitor: C=Q/V. For an ideal parallel-plate capacitor in vacuum with area A, separation d and negligible fringing, C=ε₀A/d. A dielectric filling the gap with relative permittivity κ gives C=κε₀A/d in the simplest linear medium.

The capacitor stores energy in its electric field: U=½CV²=Q²/(2C)=½QV. Increasing plate area increases capacitance, while increasing separation reduces it. In series capacitors the reciprocal capacitances add, and in parallel capacitances add. Whether insertion of a dielectric increases charge or changes voltage depends on whether the battery remains connected.

• The SI unit of capacitance is farad, F=C/V.
• Plate formulas neglect edge effects and dielectric breakdown.

Electrostatic hazards and applications

Electrostatic effects appear in photocopiers, electrostatic precipitators, capacitive sensors, powder coating and lightning. Lightning involves charge separation and rapid dielectric breakdown of air under intense fields. Earthing a device helps reduce hazardous charge accumulation and provides a route for excess charge under suitable grounding arrangements.

Electric field strengths can be substantial near sharp conductors, while shielding and controlled discharge reduce unwanted static buildup. Practical electrostatics uses both forces and potentials: forces govern motion of charged particles, potentials govern energy per unit charge, and capacitance governs electrical storage. In exams, identify whether a result asks about F, E, V, flux or stored energy before substituting formulas.

• Do not mix N/C (electric field) with volts (potential).
• Capacitance characterises geometry and medium, not stored charge alone.

Essential formulas and their conditions

Read every equation together with its stated assumptions. Symbols denote physical quantities rather than arbitrary numerical shortcuts.

Solved numericals and exam applications

Each solution uses stated approximations and is intended for method practice, not mere memorisation.

Previous-year UPSC examination concepts

The following entries paraphrase topics recorded by a third-party NDA General Ability Test past-paper index. These are not verbatim original questions or official answer keys; session labels and topic associations should be verified against UPSC’s published papers. This section is not claimed to reproduce EPFO/APFC Recruitment Test PYQs.

UPSC-style MCQs: 20 original questions

Attempt first; reveal the correct option and explanation when ready. All questions below are newly authored practice, not verbatim UPSC PYQs.

Exam traps and structured revision

• Electrostatic charge induction is charge redistribution, not creation of charge.
• Electric field is a vector; electric potential is a scalar.
• Zero enclosed charge means zero total flux, not zero field at each surface point.
• In electrostatic equilibrium E=0 inside conducting material; potential can be nonzero.
• Dipole moment points from negative to positive, unlike conventional field-line direction around a negative charge.
• The infinite-line and infinite-plane formulas rely on symmetry and idealized infinite geometry.