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CBSE Class 12 · Physics

Electrostatic Potential and Capacitance

Official NCERT chapter from Physics Part I–II (book code leph1). ExamMaster notes are original teaching at CBSE Class 12 depth.

This lesson follows the official chapter “Electrostatic Potential and Capacitance” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 12
  • Medium level
  • 12 concepts

1Electrostatic Potential

Electrostatic potential at a point is the work per unit charge to bring a test charge from a taught reference (often infinity) as taught. V is a number (volt), not a vector. Potential is energy-talk for a charge-map, not a second field-arrow.

Calling V the same as E is a miss.

Figure. Electrostatic potential at B is the external work to bring a unit test charge from A (taken at infinity in the book) to B without changing kinetic energy. Field arrows leave +Q; the work arrow runs against them, so V is higher nearer +Q.

How it works

  1. Name work per unit charge from the referencePotential.
  2. Keep the voltThe unit.
  3. Refuse a vector as this headingA number.

2Potential due to a Point Charge

Point charge: V = k q / r as taught (from infinity). Sign follows q. At r=0 the school write blows up — stay off the point. Potential of a point is a 1/r story, not 1/r^2 (that was E).

Using 1/r^2 for V is a field-steal.

Figure. For a point charge, V = kQ/r. Doubling the distance from r to 2r halves V — the marked pair on the curve. The curve does not meet the origin: V would blow up at r = 0, so the first sample sits at r = 0.20 of the axis.

How it works

  1. Copy q and rThe given.
  2. Form k q / rV.
  3. Keep 1/r, not 1/r^2The caution.

V of a point

q=2e-6 C, r=0.3 m, k=9e9. Find V.

  • k q1.8e4
  • k q / r1.8e4 / 0.3 = 6.0e4 V
  • Read60 kV as a school number

Pro tip. 1/r, not 1/r^2.

3Potential due to an Electric Dipole

Dipole potential: on axis versus equator as taught — axis is the stronger school look. V_dipole falls faster than 1/r at large r as framed. Dipole V is a pair-write, not a single kq/r.

Using kq/r for a dipole as if it were one charge is a miss.

Figure. On the dipole axis, for r much larger than a, V = k p / r^2 with p = q·2a. The dashed axis runs from the midpoint O through +q to P. Equatorial V is zero and is a different figure.

How it works

  1. Name axis or equatorWhere.
  2. Use the taught dipole-V writeThe potential.
  3. Keep it a pairTwo charges.

4Potential due to a System of Charges

System of charges: V adds as numbers (scalars) as taught. Superposition of V is easier than of E when directions fight. Three charges: add three kq/r at the point.

Adding V as vectors is a miss.

Figure. Potential is a scalar. At P add kq/r for every charge, keeping each sign. Here both charges are positive, so the two terms add. Do not add field arrows and then take a magnitude.

How it works

  1. Write each kq/r at the pointThe parts.
  2. Add as signed numbersThe net V.
  3. Keep scalar-add as the giftEasier than E.

5Equipotential Surfaces

Equipotential surfaces: V is the same on the surface as taught. E is perpendicular to them; no work to move along one. A point-charge’s equipotentials are spheres. Equipotential is a same-V look, not a field line.

A field line labelled equipotential is a swap.

Figure. Between parallel plates the field is uniform and left-to-right. Each dashed upright is an equipotential (V1 > V2 > V3 toward the negative plate). Field arrows cut those lines at right angles — that is the exam test.

How it works

  1. Name same-VThe surface.
  2. Keep E perpendicular; work 0 along itThe jobs.
  3. Refuse a field-line as this headingDifferent marks.

6Potential Energy of a System of Charges

Potential energy of a pair: U = k q1 q2 / r as taught. U is for the system, not one charge’s V. Two likes have U>0 as framed. PE is work stored in the pair.

Using V as U without the second charge is a miss.

Figure. The pair energy is the work to assemble the two charges from infinity: U = k q1 q2 / r. Same signs give U > 0 (you did work); opposite signs give U < 0 (the field did the work).

How it works

  1. Copy q1, q2, rThe given.
  2. Form k q1 q2 / rU.
  3. Keep it a system-energyTwo charges.

7Potential Energy in an External Field

PE in an external field: U = q V as taught (or −p·E for a dipole if named). External means someone else’s field. A charge at higher V has higher U if q>0.

Using kq/r when the field is “external uniform” without V is a skip.

Figure. In a uniform field a dipole has U = −p E cosθ. θ is the angle from E to p. The dashed guide is along E from −q; p runs −q to +q. Lowest U is θ = 0 (aligned); highest is θ = 180°.

How it works

  1. Name q and the external V (or p and E)The inputs.
  2. Form qV or the taught dipole writeU.
  3. Keep external as not-its-own-fieldHonest.

8Electrostatics of Conductors

Conductors in electrostatics: charge on the outer surface as taught; E=0 inside a material conductor; the surface is equipotential. A hollow with no inside-charge has E=0 in the cavity as framed. Conductor-facts are three looks, not a current-chapter.

A field-arrow inside the metal as the first claim is a miss.

Figure. In electrostatics a conductor holds excess charge on its outer surface. The cavity and the metal both have E = 0 in equilibrium. Field arrows exist only outside, leaving the surface.

How it works

  1. Name E=0 inside, charge on the skin, same VThe facts.
  2. Keep a cavity-caution if taughtHonest extra.
  3. Refuse a current as this headingElectrostatics.

9Dielectrics and Polarisation

Dielectrics and polarisation: an insulator in a field develops a taught opposite-skin look (polarisation). Dielectric constant K > 1 as framed. Polarisation is a shift-of-bits, not a free-charge flow.

Calling a dielectric a conductor because it “responds” is a miss.

Figure. A dielectric in E0 polarises: bound minus charge appears on the face toward +Q, plus on the face toward −Q. That bound pair makes Ep opposite E0, so the net field inside is E0 − Ep.

How it works

  1. Name the insulator in a fieldDielectric.
  2. Say bits shift (polarise) as taughtThe look.
  3. Keep K as the school factorThe extra.

10Capacitors and Capacitance

Capacitance: C = Q/V as taught — how much charge a pair of conductors holds per volt. Farad is the unit. A capacitor is that pair, not a battery. Larger C means more Q at the same V.

Using Q V as C is a miss.

Figure. A capacitor is two conductors holding +Q and −Q. Capacitance is the ratio C = Q/V — geometry and the medium fix C; charging does not. Q and V rise together so their ratio stays put.

How it works

  1. Form C=Q/VCapacitance.
  2. Keep the faradThe unit.
  3. Refuse a cell as this headingA store-pair.

11The Parallel Plate Capacitor

Parallel plate: C = ε0 A / d as taught (vacuum). Bigger area or smaller gap raises C. Parallel plate is the school capacitor. A dielectric later multiplies by K.

Using d in the numerator is a miss.

Figure. For a parallel-plate capacitor, C = ε0 A / d. A is the overlap area (the plate height in this side view) and d is the gap. Wider plates or a smaller gap both raise C. Field arrows sit only in the gap.

How it works

  1. Copy A and dThe given.
  2. Form ε0 A / dC.
  3. Keep A up, d down as the trendThe use.

12Effect of Dielectric on Capacitance

Dielectric in a capacitor: C becomes K C0 as taught (when it fills, disconnected-or-connected as the lesson split). The field or the charge may change — copy which was held fixed. Dielectric is a C-boost, not a new plate.

Leaving K out after “insert dielectric” is a miss.

Figure. Filling the gap with a dielectric of dielectric constant 4 multiplies capacitance by 4: C = κ C0, here 4 C0. That is the same κ that cut the field to E0/κ. The bars are to scale — four times C0 is four times as long.

How it works

  1. Name K and whether Q or V was fixedThe case.
  2. Write C=K C0 as taughtThe effect.
  3. Keep the fixed quantity honestThe caution.
Point-charge V tracks
  1. 1/r as taught — not 1/r^2
  2. 1/r^2
  3. r

Potential vs field.

Notes

  • Mapped to the official NCERT chapter “Electrostatic Potential and Capacitance”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • V=k q/r (point, from infinity)
  • U=k q1 q2 / r
  • C=Q/V
  • C=ε0 A/d (parallel plate)

Recap

Hold these pegs from the official chapter “Electrostatic Potential and Capacitance”. The wording is ExamMaster’s teaching, not a textbook recap.

Electrostatic Potential
Electrostatic potential at a point is the work per unit charge to bring a test charge from a taught reference (often infinity) as taught.
Potential due to a Point Charge
Point charge: V = k q / r as taught (from infinity).
Potential due to an Electric Dipole
Dipole potential: on axis versus equator as taught — axis is the stronger school look.
Potential due to a System of Charges
System of charges: V adds as numbers (scalars) as taught.
Equipotential Surfaces
Equipotential surfaces: V is the same on the surface as taught.
Potential Energy of a System of Charges
Potential energy of a pair: U = k q1 q2 / r as taught.

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