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Electrostatics I: Charges, Field & Gauss's Law revision notes

Every idea in the Electrostatics I: Charges, Field & Gauss's Law chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 34 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Charge and Coulomb's law

Coulomb's law
23× asked, last 2025
F=14πε0K q1q2r2F = \frac{1}{4\pi\varepsilon_0 K}\,\frac{q_1 q_2}{r^2}
Point charges. K=1K=1 in vacuum; 1/4πε0=9×1091/4\pi\varepsilon_0=9\times10^9 N m² C⁻². Like charges repel.
  • Fe/FgF_e/F_g does not depend on distance (both go as 1/r21/r^2). Electron–proton: about 103910^{39}; proton–proton: about 103610^{36}.
  • Not F/K2F/K^2. A medium divides force by KK only; the square belongs to distance. The same force in air needs distance dKd\sqrt K, not dKdK.
  • Quick method. Several charges: find each force separately, then add as vectors. At 90∘90^\circ use F12+F22\sqrt{F_1^2+F_2^2}; on one line add with signs. Charges at r=1,2,4,…r=1,2,4,\dots give a geometric series.
  • Quick method. Charge QQ split into qq and Q−qQ-q at a fixed distance: F∝q(Q−q)F\propto q(Q-q), largest for q=Q/2q=Q/2. Any unequal split gives less force.
Coulomb's law (vector form)
1× asked, last 2026
F⃗on 2=q1q24πε0 r⃗2−r⃗1∣r⃗2−r⃗1∣3\vec F_{\text{on }2} = \frac{q_1 q_2}{4\pi\varepsilon_0}\,\frac{\vec r_2-\vec r_1}{|\vec r_2-\vec r_1|^3}
Force on q2q_2 due to q1q_1. Divide by r3r^3, not r2r^2; the signs of qq fix the direction.
Quantisation of charge
3× asked, last 2026
q=± ne,e=1.6×10−19 Cq = \pm\, n e,\qquad e = 1.6\times10^{-19}\ \text{C}
nn is a whole number. A charged drop carries n=q/en=q/e extra or missing electrons.
  • Charge is additive (algebraic sum) and conserved in every isolated process; rubbing only transfers electrons. A body at +q+q has lost q/eq/e electrons, so its mass falls by (q/e)me(q/e)m_e.
Sharing on contact
4× asked, last 2025
q1′=q2′=q1+q22q_1' = q_2' = \frac{q_1+q_2}{2}
Identical conductors only; signs included. Update the moving sphere after each touch.
  • Not Q/2Q/2 on the second sphere touched. R already holds Q/2Q/2. P, S at QQ with force FF; neutral R touches P then S: P =Q/2=Q/2, S =3Q/4=3Q/4, so F′=3F/8F'=3F/8.
Two hanging charged balls
4× asked, last 2024
tan⁡θ=Femg,x3=q2 l2πε0 mg\tan\theta = \frac{F_e}{mg},\qquad x^3 = \frac{q^2\, l}{2\pi\varepsilon_0\, m g}
Threads of length ll, separation xx, small θ\theta so tan⁡θ≈x/2l\tan\theta\approx x/2l.
θ\thetallTTmgmgFeF_exx
Each ball: TT, mgmg and FeF_e close up, so tan⁡θ=Fe/mg\tan\theta=F_e/mg; small θ\theta: tan⁡θ≈x/2l\tan\theta\approx x/2l
  • Same angle in a liquid only if K=ρ/(ρ−ρl)K=\rho/(\rho-\rho_l) (ρ\rho, ρl\rho_l: ball and liquid densities): force ÷K\div K, weight ×(1−ρl/ρ)\times(1-\rho_l/\rho) by buoyancy.
Also remember
  • Moving insulated bodies (fuel tankers, aircraft) pick up charge by friction with air. A metal chain to the ground drains it and prevents sparks.
  • Not SI by default: 9.19.1 V/cm =910=910 V/m, 11 dyne/C =10−5=10^{-5} N/C, 100100 mg =10−4=10^{-4} kg. Many wrong options are exactly a power of ten off.

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Practise Electrostatics I: Charges, Field & Gauss's Law

29 more concepts in 5 topics

Electric field, Charge distributions and conductors, Electric dipole and Flux and Gauss's law, plus ideas from potential basics. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Electric field

  • Field of point charges13×
  • Continuous charge
  • Null point of two charges5×
  • Charged bob in a field11×
  • Charge moving across a uniform field8×
  • Also remember1

Charge distributions and conductors

  • Infinite line charge8×
  • Finite rod (perpendicular distance r)2×
  • Point on the rod's own line2×
  • Ring on its axis4×
  • Arc at its centre3×
  • Disc on its axis1×
  • Infinite sheet and conductor surface15×
  • Spherical shell10×
  • Uniformly charged solid sphere5×
  • Long charged cylinder2×
  • Conductor in equilibrium8×

Electric dipole

  • Dipole moment1×
  • Short dipole: axial and equatorial7×
  • Short dipole: any point
  • Exact axial field6×
  • Dipole in a uniform field10×
  • Work to rotate a dipole
  • Small oscillations2×
  • Dipole in a non-uniform field2×

Flux and Gauss's law

  • Flux through a flat surface12×
  • Flux through a disc or curved surface
  • Gauss's law28×
  • Charge and a cube8×
  • Electric field lines2×

Also asked here: potential basics

  • Key points4

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Practise Electrostatics I: Charges, Field & Gauss's Law

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