Schooling · Class 12 · Physics · Electrostatic Potential and Capacitance · Chapter on a page
CBSE Class 12 · Physics · NCERT Physics Part-I
Electrostatic Potential and Capacitance: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Electric potential at a point is the…
- Potential difference between two…
- Equipotential surfaces are surfaces…
- The potential due to a point charge…
- Capacitance C of a conductor is…
- For a parallel plate capacitor with…
- Energy stored in a charged capacitor…
- Formulas and facts
- Potential due to a point charge
- Potential energy of two charges
- Relation between field and potential
- Capacitance definition
- Parallel plate capacitor
- Effect of dielectric
- Energy stored
- Watch out for
- Treating potential as a vector
- Using the series formula for…
- Forgetting the sign of potential for…
- Assuming charge changes when a…
- Ignoring units when calculating…
What this chapter is about
This chapter builds on your understanding of electric charges and fields by introducing two related quantities: electrostatic potential and capacitance. While the previous chapter focused on the electric field as a vector quantity, this chapter presents electric potential as a scalar quantity that simplifies many calculations. You learn how work done in moving charges relates to potential energy and potential difference.
Key ideas
- Electric potential at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. It is a scalar quantity measured in volts (V), where 1 V = 1 J/C.
- Potential difference between two points equals the work done per unit charge in moving a test charge between those points. Current flows from higher to lower potential.
- Equipotential surfaces are surfaces where every point has the same potential. The electric field is always perpendicular to an equipotential surface, and no work is done when a charge moves along such a surface.
- The potential due to a point charge Q at distance r is V = kQ/r = Q/(4πε₀r), where k = 9 × 10⁹ N m² C⁻².
- Capacitance C of a conductor is defined as C = Q/V, the ratio of charge stored to potential. The SI unit is farad (F), where 1 F = 1 C/V.
- For a parallel plate capacitor with plate area A and separation d, the capacitance is C = ε₀A/d in vacuum, and C = Kε₀A/d when a dielectric of constant K fills the gap.
- Energy stored in a charged capacitor is U = (1/2)CV² = (1/2)QV = Q²/(2C).
- Capacitors in parallel add directly: C_total = C₁ + C₂ + ... . Capacitors in series combine as 1/C_total = 1/C₁ + 1/C₂ + ... .
Formulas and facts to remember
- Potential due to a point charge: V = Q/(4πε₀r) — potential decreases as 1/r from a point charge.
- Potential energy of two charges: U = Q₁Q₂/(4πε₀r) — the work needed to assemble the configuration.
- Relation between field and potential: E = −dV/dr along the direction of the field — field points from high to low potential.
- Capacitance definition: C = Q/V — larger capacitance means more charge stored per volt.
- Parallel plate capacitor: C = ε₀A/d — capacitance increases with area and decreases with separation.
- Effect of dielectric: C becomes KC₀, where K is the dielectric constant and C₀ is capacitance without the dielectric.
- Energy stored: U = (1/2)CV² — this energy resides in the electric field between the plates.
- Series combination: 1/C_eq = 1/C₁ + 1/C₂ — equivalent capacitance is smaller than the smallest individual capacitor.
- Parallel combination: C_eq = C₁ + C₂ — equivalent capacitance is the sum of individual capacitances.
Common mistakes
- Treating potential as a vector → Potential is a scalar; add contributions with their signs, not as vectors.
- Using the series formula for parallel capacitors → Remember: series uses reciprocals, parallel uses direct addition.
- Forgetting the sign of potential for negative charges → V = kQ/r includes the sign of Q; negative charges give negative potential.
- Assuming charge changes when a disconnected capacitor gets a dielectric → Charge stays constant when disconnected; potential and energy change instead.
- Ignoring units when calculating capacitance → Keep distances in metres and charges in coulombs to get farads directly.
Quick revision
- Electric potential is work per unit charge; it is a scalar measured in volts.
- Field points from high potential to low potential and is perpendicular to equipotential surfaces.
- Capacitance C = Q/V; a dielectric increases capacitance by factor K.
- Series capacitors: same charge, voltages add; parallel capacitors: same voltage, charges add.
- Energy stored in a capacitor is (1/2)CV², residing in the electric field.