ElectromagnetismTop Priority (3-4 Qs in JEE)

Electrostatics Formulas

Coulomb's law, Gauss's theorem, electric field, potential, dipoles, and electrostatic potential energy.

8 Formulas•817+ Questions in Bank•

Concept Diagram

Parallel Plate Capacitor & Dielectric

Parallel plates of area A and separation d, uniform electric field E = σ/ε₀, and dielectric polarization.

Core Formulas & Mathematical Identities

Coulomb's Law & Permittivity

F = \frac{1}{4\pi\varepsilon_0 \varepsilon_r} \frac{q_1 q_2}{r^2}, \quad \frac{1}{4\pi\varepsilon_0} \approx 9 \times 10^9 \text{ N m}^2/\text{C}^2

Inverse-square force between point charges in medium of relative permittivity ε_r.

Examiner Tip: Force in medium of dielectric constant K is F_air / K.

Gauss's Law & Electric Flux

\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0}

Total electric flux through closed Gaussian surface equals enclosed charge divided by ε₀.

Examiner Tip: Charges outside the Gaussian surface contribute zero net flux.

Electric Field of Standard Geometries

E_{\text{wire}} = \frac{2k\lambda}{r}, \quad E_{\text{sheet}} = \frac{\sigma}{2\varepsilon_0}, \quad E_{\text{ring, axis}} = \frac{kqx}{(R^2 + x^2)^{3/2}}

Field formulas derived via Gauss's law for high-symmetry distributions.

Examiner Tip: Maximum field on ring axis occurs at x = R / √2.

Electric Dipole Fields & Torque

E_{\text{axial}} = \frac{2kp}{r^3}, \quad E_{\text{equatorial}} = \frac{kp}{r^3}, \quad \vec{\tau} = \vec{p} \times \vec{E}, \quad U = -\vec{p} \cdot \vec{E}

Field and potential energy of electric dipole p = q(2a) at distant points (r >> a).

Examiner Tip: Axial field is exactly twice the equatorial field: E_axial = 2 E_eq.

Relation Between Field and Potential

\vec{E} = -\vec{\nabla} V = -\left(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k}\right), \quad \Delta V = -\int \vec{E} \cdot d\vec{r}

Electric field points in direction of steepest decrease of potential.

Examiner Tip: Equipotential surfaces are always perpendicular to electric field lines.

Uniform Solid Dielectric Sphere (Field & Potential)

r \le R: \; E(r) = \frac{k Q r}{R^3} = \frac{\rho r}{3\varepsilon_0}, \quad V(r) = \frac{kQ}{2R^3}(3R^2 - r^2) \implies V_{\text{center}} = 1.5 \, V_{\text{surface}}

Linear internal electric field and parabolic internal potential distribution for uniform volume charge density ρ.

Examiner Tip: Potential at the exact center of a uniformly charged solid non-conducting sphere is 1.5 times the surface potential.

Electrostatic Self-Energy of Spheres

U_{\text{conducting shell}} = \frac{k Q^2}{2R}, \quad U_{\text{solid insulating sphere}} = \frac{3}{5}\frac{k Q^2}{R}

Work done in assembling a continuous spherical charge distribution against mutual electrostatic repulsion.

Examiner Tip: For concentric shells: total energy is sum of individual self-energies plus mutual interaction energy.

Earthing of Concentric Conducting Shells

V_{\text{earthed shell}} = 0 \implies \sum_{i} \frac{k q_i}{R_{\text{effective}}} = 0

When a conducting shell is grounded to Earth, charge flows to/from Earth until its net electrostatic potential becomes exactly zero.

Examiner Tip: Earthing a shell does NOT mean its charge is zero; it means its net potential V = 0.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Electrostatics

•Electric field is zero inside a conductor, but electric potential is CONSTANT and equals the surface potential.
•Electric potential due to dipole on equatorial plane is ZERO, but electric field is NON-ZERO.

Fundamental Theory & Core Concepts

4 Topics

1Fundamental Charge Properties & Coulomb Interactions

›Charge Properties: Quantization (q = ±n·e, where e = 1.602 × 10⁻¹⁹ C), conservation of charge in isolated systems, and relativity invariance (charge magnitude does not vary with velocity, unlike relativistic mass).
›Coulomb's Law: Force acts strictly along the line joining two stationary point charges: F = (1 / 4πε) · (q₁q₂ / r²). In a dielectric medium of relative permittivity ε_r (dielectric constant K), F_med = F_air / K.
›Principle of Superposition: The resultant electrostatic force on any charge equals the vector sum of individual pairwise forces exerted by all other charges: F_net = Σ F_i. Pairwise interaction between any two charges is unaffected by the presence of other charges.

2Electric Field Lines & Gauss's Theorem Principles

›Field Line Properties: Start on positive charges and terminate on negative charges (or infinity). Never form closed loops because electrostatic field is conservative. Tangent gives field direction; density of lines represents electric field magnitude. Two field lines never intersect.
›Gauss's Law: Total electric flux Φ_E = ∮ E · dA = Q_enclosed / ε₀. Applicable to any arbitrary closed Gaussian surface.
›Crucial Gauss Nuance: Electric field E in the flux integral is the resultant field caused by ALL charges (both inside and outside the Gaussian surface), whereas the net flux depends solely on the algebraic sum of enclosed charges Q_enclosed.
›Symmetry Applications: Infinite wire E = 2kλ/r; Infinite thin non-conducting sheet E = σ / (2ε₀); Thin conducting plate E = σ / ε₀ (charge distributed over two faces).

3Electric Potential, Conservative Work & Equipotential Surfaces

›Potential Definition: Work done by external agent without acceleration to bring unit positive test charge from infinity to that point: V(r) = -∫_∞^r E · dr. For point charge: V = kq / r.
›Relation Between Field and Potential: E = -∇V = -(∂V/∂x i + ∂V/∂y j + ∂V/∂z k). Electric field vector always points in the direction of maximum rate of decrease of electric potential.
›Equipotential Surfaces: Surfaces where potential is constant everywhere. Electric field is always perpendicular to equipotential surfaces at every point. Work done moving any charge along an equipotential surface is zero (W = q·ΔV = 0).
›Potential Energy: For two charges U = k·q₁·q₂ / r. For a system of N point charges, total potential energy is the sum over all N(N-1)/2 distinct pairs: U_total = Σ_{i < j} k·q_i·q_j / r_ij.

4Electrostatics of Conductors & Cavities

›Conductor in Electrostatic Equilibrium: 1) E = 0 everywhere inside the conducting material. 2) Net interior charge density ρ = 0; any excess charge resides exclusively on the outer boundary surface. 3) The entire body and surface of conductor is an equipotential region (V_inside = V_surface).
›Surface Field & Pressure: Field just outside a charged conductor is perpendicular to surface: E = σ / ε₀. Electrostatic outward pressure on surface: P = σ² / (2ε₀) = (1/2) ε₀ E².
›Electrostatic Shielding & Cavities: Electric field inside an uncharged cavity enclosed within a conductor is identically zero, irrespective of external fields or charges on the conductor exterior. When a charge +q is placed inside cavity, -q is induced on cavity inner wall and +q on conductor outer surface.

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