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Electrostatic Potential and Capacitance Class 12 Physics Formula Sheet & Quick Revision 2026-27

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Electrostatic Potential and Capacitance — Class 12 Physics Formula Sheet & Quick Revision
A compact, exam-focused revision resource covering electric potential, potential energy, conductors, dielectrics, capacitance, capacitor combinations and energy stored in a capacitor.

Class 12 Physics Chapter 2 — Quick Revision

This formula sheet follows the CBSE 2026–27 Chapter 2 scope: electric potential and potential difference; potential due to a point charge, dipole and system of charges; equipotential surfaces; electrostatic potential energy; conductors and insulators; free and bound charges; dielectrics and polarization; capacitors and capacitance; series and parallel combinations; parallel-plate capacitance with and without dielectric; and energy stored in a capacitor.

Best use: Revise the formula tables first, then use the “Exam Traps” and “30-Second Self-Check” sections without opening your notes.

1. Electric Potential — Core Formulas

Concept Formula / Result Remember
Electric potential V = W/q0 Work done per unit positive test charge in bringing it from infinity.
Potential difference VB − VA = −∫AB E·dl For electrostatics, potential difference is path independent.
Potential due to a point charge V = (1/4πε0) q/r V is a scalar; retain the sign of q.
Potential due to many charges V = (1/4πε0) Σ(qi/ri) Add potentials algebraically, not as vectors.
Relation between field and potential E = −dV/dr (one-dimensional/radial case) The electric field points toward decreasing potential.

Potential: Fast Exam Facts

  • Electric potential is a scalar quantity.
  • Its SI unit is volt (V), where 1 V = 1 J C−1.
  • Potential can be positive, negative or zero.
  • V = 0 at a point does not necessarily mean E = 0 there.
  • For a positive point charge, V is positive when the reference is V = 0 at infinity.
  • For a negative point charge, V is negative under the same reference.

2. Electric Potential Due to a Dipole

Dipole moment:

p = qd

Here d is the separation vector magnitude from the negative charge to the positive charge; the direction of p is from −q to +q.

Potential of a short dipole at a point far from the dipole:

V = (1/4πε0) (p cosθ / r2)

Use the far-field condition: r is much larger than the dipole separation.

Important Dipole Positions

  • Axial line: θ = 0° or 180°, so cosθ = ±1.
  • Equatorial line: θ = 90°, so cosθ = 0 and the ideal dipole potential is zero.
  • At a point where V = 0, the electric field may still be non-zero.

3. Equipotential Surfaces

  • An equipotential surface has the same potential at every point.
  • Work done in moving a charge along an equipotential surface is zero.
  • The electric field is perpendicular to an equipotential surface.
  • Two equipotential surfaces cannot intersect.
  • Where equipotential surfaces are closer together, the magnitude of the electric field is larger.

4. Electrostatic Potential Energy

Situation Formula / Result Exam note
Charge q in potential V U = qV Use the signed value of q and the relevant potential.
Two point charges U = (1/4πε0) q1q2/r Positive for like charges; negative for unlike charges, with infinity as zero reference.
System of point charges U = (1/4πε0) Σpairs(qiqj/rij) Count each distinct pair once.
Dipole in uniform electric field U = −pE cosθ = −p·E Minimum energy occurs when p is parallel to E.

5. Conductors — Quick Revision

  • In electrostatic equilibrium, the electric field inside the conducting material is zero.
  • Excess charge on an isolated conductor resides on its surface.
  • The conductor is an equipotential body in electrostatic equilibrium.
  • The electric field at the surface of a conductor is normal to the surface.
  • For a conductor, charge redistribution continues until electrostatic equilibrium is reached.
Common trap: “Electric field is zero” must be interpreted carefully. In this chapter, the standard statement is that the field inside the conducting material is zero when the conductor is in electrostatic equilibrium.

6. Dielectrics and Polarization

  • A dielectric is an insulating material that becomes polarized when placed in an electric field.
  • Polarization produces an induced field that opposes the applied field inside the dielectric.
  • For a parallel-plate capacitor completely filled with a dielectric of dielectric constant K, capacitance increases by a factor K.
  • K = C/C0 for the same capacitor when the dielectric completely fills the space.

7. Capacitance — Core Formulas

Concept Formula Remember
Capacitance C = Q/V SI unit: farad (F).
Parallel-plate capacitor in vacuum C0 = ε0A/d A = plate area; d = separation.
Parallel-plate capacitor with dielectric C = Kε0A/d = εA/d K = dielectric constant; ε = Kε0.
Capacitance ratio C/C0 = K Only when the dielectric fully fills the relevant space.

How Geometry Changes Capacitance

  • If plate area A doubles, capacitance doubles.
  • If separation d doubles, capacitance becomes half, for the same medium.
  • If a dielectric of constant K completely fills the gap, capacitance becomes K times the vacuum value.

8. Capacitors in Series

1/Ceq = 1/C1 + 1/C2 + ... + 1/Cn

  • Same charge: Q is the same on each capacitor in a simple series combination.
  • Potential differences add: V = V1 + V2 + ...
  • Voltage division: for capacitors in series, Vi = Q/Ci.
  • The equivalent capacitance is smaller than the smallest individual capacitance in a simple series combination.
Two-capacitor shortcut:

Ceq = (C1C2)/(C1 + C2)

9. Capacitors in Parallel

Ceq = C1 + C2 + ... + Cn

  • Same potential difference: V is the same across each capacitor.
  • Charges add: Q = Q1 + Q2 + ...
  • For a simple parallel combination, the equivalent capacitance is larger than the largest individual capacitance.

10. Energy Stored in a Capacitor

U = ½CV2 = ½QV = Q2/(2C)

All three forms represent the same stored electrostatic energy. Choose the form that matches the quantities given in the question.

Given / held constant Useful form Quick implication
Q and C U = Q2/(2C) At fixed Q, increasing C decreases U.
C and V U = ½CV2 At fixed V, increasing C increases U.
Q and V U = ½QV Useful when both charge and potential difference are known.

11. Dielectric Inserted: Battery Connected vs Isolated

These comparison questions are common because the condition changes what remains constant.

Quantity Battery remains connected Battery disconnected / isolated
Capacitance C → KC C → KC
Charge Q → KQ Q = constant
Potential difference V = constant V → V/K
Stored energy U → KU U → U/K
Memory rule: Connected battery fixes V. Disconnected capacitor fixes Q.

12. Constants and SI Units

Quantity Value / Unit
Permittivity of free space ε0 ≈ 8.85 × 10−12 F m−1
Coulomb constant 1/(4πε0) ≈ 9 × 109 N m2 C−2
Electric potential volt (V) = joule/coulomb
Capacitance farad (F) = coulomb/volt
Potential energy joule (J)

13. Formula Selection Guide for Numericals

Question asks for Start with
Potential due to a point chargeV = (1/4πε0)q/r
Potential due to several chargesV = (1/4πε0)Σ(qi/ri)
Potential energy of two chargesU = (1/4πε0)q1q2/r
Dipole energy in uniform fieldU = −pE cosθ
Parallel-plate capacitanceC = ε0A/d or C = Kε0A/d
Series capacitors1/Ceq = Σ(1/Ci)
Parallel capacitorsCeq = ΣCi
Energy storedU = ½CV² = ½QV = Q²/(2C)

14. Exam Traps to Avoid

  1. Potential is scalar: do not add electric potentials as vectors.
  2. V = 0 does not imply E = 0: always distinguish potential from electric field.
  3. Series vs parallel: series → same Q; parallel → same V.
  4. Dielectric insertion: first decide whether the battery is connected or disconnected.
  5. Energy formula: do not use ½CV² automatically when V is not the fixed/known quantity.
  6. Dipole potential: the short-dipole expression V ∝ cosθ/r² is a far-field result.
  7. Potential energy of a pair: keep the signs of q1 and q2.
  8. Capacitance depends on geometry and medium: it is not simply “charge stored” by itself.
  9. Conductor statement: specify electrostatic equilibrium when stating that the field inside the conducting material is zero.
  10. Units: check whether the final answer should be in V, F or J before submitting a numerical.

15. 30-Second Self-Check

  • Can I write the potential due to one point charge?
  • Can I add potentials from several charges correctly?
  • Can I explain why potential is scalar?
  • Can I distinguish an equipotential surface from a zero-potential point?
  • Can I write the potential energy of two charges?
  • Can I write U = −pE cosθ for a dipole in a uniform field?
  • Can I state the electrostatic condition inside a conductor?
  • Can I write C = ε0A/d and the dielectric version?
  • Can I immediately identify same-Q in series and same-V in parallel?
  • Can I choose the correct energy formula for a capacitor?
  • Can I distinguish connected-battery and isolated-capacitor conditions?

16. Continue Your Chapter 2 Preparation

17. Syllabus & Source Note

The CBSE 2026–27 Physics curriculum places Chapters 1 and 2 under Unit I: Electrostatics, which carries 16 marks at the unit level. The curriculum lists the Chapter 2 topics used on this page and specifically states that energy stored in a capacitor is formula-only, with no derivation required in the listed syllabus scope. View the official CBSE Physics 2026–27 curriculum.

For the current Class XII 2026–27 sample-question-paper and marking-scheme resources, use the official CBSE Academic page: CBSE Class XII 2026–27 Sample Question Papers & Marking Schemes.

Revision target: You should be able to reproduce the major formulas from memory, explain when each formula applies, and identify the fixed quantity before solving capacitor/dielectric questions.

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