Electrostatics opens Class 12 Physics by asking what happens between charges at rest, and the entire chapter builds outward from one single force law into fields, potential, and finally the energy stored in a capacitor.
Coulomb's law gives the force between two point charges. Electric field is simply that force per unit test charge, which lets you describe the space around a charge independently of whatever second charge you eventually place there. Gauss's law then reframes the same physics using symmetry and flux, turning problems that would need difficult integration into a few lines of algebra whenever the charge distribution is symmetric enough. Capacitors close the chapter by asking how much charge — and therefore how much energy — a system of conductors can store.
Core electrostatics formulae
| Quantity | Formula |
|---|---|
| Coulomb's law | F = kq₁q₂/r², k = 1/4πε₀ |
| Electric field due to a point charge | E = kq/r² |
| Electric potential due to a point charge | V = kq/r |
| Relation between E and V | E = −dV/dr |
| Gauss's law | ∮E·dA = qenc/ε₀ |
| Capacitance of a parallel plate capacitor | C = ε₀A/d |
| Capacitors in series | 1/C = 1/C₁ + 1/C₂ + ... |
| Capacitors in parallel | C = C₁ + C₂ + ... |
| Energy stored in a capacitor | U = ½CV² |
Topics covered
- Coulomb's law — the force law between point charges, and its vector form
- Electric field — field due to a point charge, a dipole, and a system of charges, using superposition
- Electric field lines — their properties, and what their density and direction represent physically
- Electric dipole — dipole moment, field on the axial and equatorial lines, and torque in a uniform field
- Electric potential and potential energy — the scalar alternative to the vector electric field, and how they connect
- Equipotential surfaces — why they're always perpendicular to field lines, with no exceptions
- Gauss's law — electric flux, and its application to spheres, cylinders and infinite sheets
- Capacitors and capacitance — parallel plate capacitors, and the effect of a dielectric
- Combination of capacitors — series and parallel rules, and mixed-combination problem solving
- Energy stored in a capacitor — and energy density in the electric field
Why this chapter matters
In NEET and JEE, Gauss's law applications (field due to a charged sphere, cylinder, or infinite sheet) and capacitor combination numericals are among the highest-frequency question types in the entire electricity and magnetism section, since this chapter's tools reappear constantly through Current Electricity and Magnetic Effects. Dipole-in-a-field questions testing torque and potential energy are also a recurring favourite.
For Class 12 boards, expect a Gauss's law derivation for a specific symmetric charge distribution and a numerical on capacitors in a mixed series-parallel combination.
Mistakes students make in this chapter
- Applying Gauss's law to an asymmetric charge distribution. It only simplifies calculation when the charge distribution has enough symmetry (spherical, cylindrical or planar) to make the electric field constant over a chosen Gaussian surface — without that symmetry it's still true but not useful.
- Confusing electric field and electric potential as interchangeable. Field is a vector; potential is a scalar. A point can have zero field but nonzero potential, or vice versa — a classic exam trap using the midpoint between two equal like charges.
- Forgetting a dielectric increases capacitance. Inserting a dielectric between capacitor plates always increases capacitance by the dielectric constant factor, never decreases it.
- Mixing up series and parallel capacitor rules with resistor rules. Capacitors in series combine like resistors in parallel (reciprocals add) and vice versa — this reversal relative to resistors is a very commonly confused point.
- Assuming equipotential surfaces can intersect field lines at any angle. They are always perpendicular to field lines, with no exception — if they weren't, work would be done moving along the equipotential surface, contradicting its definition.
Worked example: the disconnected-battery trap
- Decide what is held fixed. The battery is gone, so no charge can enter or leave the plates. Charge Q is the conserved quantity here — not voltage. Getting this one line right decides the whole question.Q = C₀V₀ → stays constant
- Capacitance rises by the factor K. The dielectric reduces the net field between the plates for the same charge, so the plates hold the same charge at a lower potential.C = K·C₀
- Potential drops. Using Q = CV with Q fixed and C now K times larger:V = Q/C = C₀V₀ / (K·C₀) = V₀ / K
- Field drops by the same factor, since separation d has not changed.E = V/d = E₀ / K
- Energy drops. With Q fixed, use the form of the energy equation written in terms of Q, not V:U = Q²/2C = Q²/(2K·C₀) = U₀ / K
What the notes contain
The PDF derives the electric field due to a charged sphere, an infinite sheet and a long charged cylinder using Gauss's law, works through dipole field and torque derivations, and covers capacitor combination problems including mixed networks with a dielectric inserted partway.
How to use this: build the concept from these notes first, then do one quick NCERT pass before the exam for exact wording and diagram labels, and spend whatever time is left on previous year questions.
Questions
Why is Gauss's law useful if Coulomb's law already gives the field?
For symmetric charge distributions, Gauss's law turns what would be a difficult direct integration using Coulomb's law into a straightforward algebraic calculation, by exploiting the symmetry to pull the field outside the flux integral. Both approaches are shown side by side in the PDF for comparison.
Can electric field be zero while potential is nonzero at the same point?
Yes — exactly midway between two equal positive charges, for instance, the field contributions cancel to zero while the potential contributions add up to a nonzero value. This distinction is worked through with a diagram.
Why does inserting a dielectric always increase capacitance?
A dielectric polarises in response to the field between the plates, reducing the net field for the same charge and therefore allowing more charge to be stored for the same voltage — increasing capacitance by the dielectric constant.
Does this cover mixed series-parallel capacitor networks?
Yes, with a systematic method for reducing complex networks step by step, plus a worked example including a dielectric inserted in one branch.
All other chapters
Every chapter of Class 11 and Class 12 Physics, Chemistry and Biology — each with its own notes and PDF.