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Portion 3 · Revision flow · Electric Charges and Fields
Charge basics
  1. 01Scalar quantity
  2. 02Unit Coulomb
  3. 03Dimension [AT]
  4. 04Quantized q = ±ne
  5. 05Always conserved
Gold-leaf electroscope
  1. 01Charged body touches disc
  2. 02Charge flows down rod
  3. 03Both leaves get same charge
  4. 04Leaves repel → diverge
Coulomb's law chain
  1. 01F ∝ q₁q₂
  2. 02F ∝ 1/r²
  3. 03F = kq₁q₂/r²
  4. 04k = 1/4πε₀ = 9×10⁹
  5. 05Vector form F₁₂ = −F₂₁
Dielectric constant
  1. 01Force in air F₀
  2. 02Force in medium Fₘ
  3. 03K = F₀/Fₘ
  4. 04K = εₘ/ε₀
  5. 05Water K = 80
Electric field
  1. 01Source charge makes field
  2. 02Test charge feels force
  3. 03E = F/q₀
  4. 04Point charge E = kQ/r²
  5. 05Vector, unit NC⁻¹
Dipole formulas
  1. 01p = q × 2l
  2. 02Axial E = 2kp r/(r²−l²)²
  3. 03Short dipole axial = 2kp/r³
  4. 04Equatorial = kp/r³
  5. 05E_axial = 2E_eq
Torque cases
  1. 01τ = pE sin θ
  2. 02θ = 0° stable, τ = 0
  3. 03θ = 90° τ max = pE
  4. 04θ = 180° unstable, τ = 0
Gauss's theorem
  1. 01Draw Gaussian surface
  2. 02Flux = ∮E·dS
  3. 03θ = 0° on sphere
  4. 04E × 4πr² = q/ε₀
  5. 05Φ = q/ε₀
Gauss applications
  1. 01Line charge E = λ/2πε₀r
  2. 02Plane sheet E = σ/2ε₀
  3. 03Shell outside E = kq/r²
  4. 04Shell surface E = σ/ε₀
  5. 05Shell inside E = 0
Field line rules
  1. 01Start on +, end on −
  2. 02Never cross
  3. 03No closed loops
  4. 04⊥ to conductor surface
  5. 05Zero inside conductor
Suggestions · Missing points · Electric Charges and Fields

Every question in this chapter has its Remember box, exam tip, common mistake and quick revision points. Nothing missing.

Quick facts · Electric Charges and Fields
SI unit of charge
Coulomb (C)
Dimensional formula of charge
[AT]
Elementary charge e
1.6 × 10⁻¹⁹ C
Electrostatic constant k
9 × 10⁹ N m² C⁻²
Permittivity of free space ε₀
8.854 × 10⁻¹² C² N⁻¹ m⁻²
Dimensional formula of ε₀
[M⁻¹L⁻³T⁴A²]
K for water / air / vacuum
80 / 1.00059 / 1
E field unit
N C⁻¹, dimension [MLT⁻³A⁻¹]
Dipole moment
p = q × 2l, unit C m
Torque on dipole
τ = pE sin θ
Flux unit
N m² C⁻¹, dimension [ML³T⁻³A⁻¹]
1 Coulomb (CGS)
3 × 10⁹ statcoulomb (esu)
One-minute recaps
Q1. Explain the term electrostatics. Give some applications.
  • Study of charges at rest
  • Photocopier, capacitor, precipitator
  • Atomic structure, spray painting
Q2. What is an electric charge?
  • Causes electric force
  • Scalar
  • Coulomb (C)
  • [AT]
Q3. What is an electroscope? Discuss the working of a Gold-leaf Electroscope.
  • Detects presence and nature of charge
  • Disc → rod → gold leaf
  • Same charge = diverge more
  • Opposite charge = diverge less
Q4. Explain the methods of charging a material.
  • Conduction = touch and share
  • Friction = rubbing
  • Glass + silk, carpet, comb, hot iron
  • Induction excluded
Q5. Define conservation of electric charge.
  • Net charge of isolated system constant
  • Friction: +q − q = 0
  • Decay: 92 = 90 + 2
  • Pair production and annihilation: 0 = 0
Q6. Explain Quantization of Electric Charge.
  • q = ±ne
  • e = 1.6 × 10⁻¹⁹ C
  • n must be an integer
  • 1 C = 6.25 × 10¹⁸ electrons
Q7. Compare the properties of electric charge with that of the mass of a body.
  • Sign
  • Quantization
  • Conservation
  • Velocity dependence
  • Fundamental vs derived
Q8. Explain Coulomb's law.
  • F ∝ q₁q₂
  • F ∝ 1/r²
  • F = kq₁q₂/r²
  • k = 1/4πε₀
Q9. What is relative permittivity (Dielectric Constant)?
  • K = F₀/Fₘ
  • K = εₘ/ε₀
  • No unit
  • Water 80, metals ∞
Q10. What are the characteristics of Electrostatic force (Coulomb's force)?
  • Central
  • Spherically symmetric
  • Inverse square
  • Two-body
  • Conservative
Q11. Show vector form of Coulomb's law in accordance to Newton's 3rd law.
  • F₂₁ along r̂₁₂
  • r̂₁₂ = −r̂₂₁
  • F₁₂ = −F₂₁
  • Position vector form has |r|³
Q12. Define one Coulomb.
  • q₁ = q₂ = 1 C
  • r = 1 m
  • F = 9 × 10⁹ N
  • 1 C = 3 × 10⁹ esu
Q13. Compare electrostatic force and gravitational force.
  • Both long range, inverse square, central, conservative
  • Electrostatic: ± and medium dependent
  • Gravitational: always attractive, weakest
Q14. Show and explain Superposition Principle of electric charge.
  • Net force = vector sum
  • Each pair uses Coulomb's law
  • Summation form with |r₀ − rᵢ|³
Q15. What is meant by continuous charge distribution? Mention and explain different types of charge densities.
  • λ = q/L
  • σ = q/S
  • ρ = q/V
  • dq = λdl, σdS, ρdV
Q16. What do you understand by electric field? Define Electric field intensity.
  • Region of influence
  • E = F/q₀
  • Vector, NC⁻¹
  • Uniform vs non-uniform
Q17. Derive an expression for Electric field intensity due to a point charge at origin.
  • E = F/q₀
  • F = kQq₀/r²
  • E = kQ/r² r̂
  • E ∝ 1/r²
Q18. Define Electric field line. Explain its various properties.
  • Start +, end −
  • Tangent gives direction
  • Never cross
  • Density = strength
  • No closed loops
Q19. What is an electric dipole? Define dipole moment.
  • Two equal opposite charges
  • p = q × 2l
  • Vector, − to +
  • Unit Cm
Q20. Find the electric field intensity at a point on the axial line of a dipole.
  • E₊ at (r−l)
  • E₋ at (r+l)
  • Subtract
  • 4rl in numerator
  • Short dipole: 2kp/r³
Q21. Find electric field intensity at a point on the equatorial line (broad side position) of a dipole.
  • Distance √(r²+l²)
  • Sinθ cancels, cosθ adds
  • E = kp/(r²+l²)^{3/2}
  • Short dipole kp/r³
  • Opposite to p
Q22. Show that the torque experienced by an electric dipole is the cross product of dipole moment and electric field.
  • Couple of forces qE
  • Arm = 2l sinθ
  • τ = pE sinθ
  • τ = p × E
  • Max at 90°
Q23. What do you understand by area vector? What is electric flux?
  • dS⃗ = dS n̂ outward
  • dΦ = E dS cosθ
  • Φ = ∮E·dS
  • Unit Nm²C⁻¹
Q24. State Gauss's theorem and prove it.
  • Φ = q/ε₀
  • Spherical Gaussian surface
  • θ = 0°
  • ∮dS = 4πr²
  • E×4πr² = q/ε₀
Q25. Derive Coulomb's law from Gauss's theorem.
  • Gaussian sphere on q₁
  • E = kq₁/r²
  • F = q₂E
  • F = kq₁q₂/r²
Q26. Electric field at a point near an infinitely long uniformly charged wire (application of Gauss's theorem).
  • Cylindrical Gaussian surface
  • q = λl
  • Caps give zero flux
  • E(2πrl) = λl/ε₀
  • E = λ/2πε₀r
Q27. Electric field intensity due to a uniformly charged infinite plane sheet.
  • Cylinder through sheet
  • q = σA
  • Φ = 2EA
  • E = σ/2ε₀
  • Capacitor: σ/ε₀ inside, 0 outside
Q28. Electric field intensity due to a uniformly charged thin spherical shell.
  • Outside: kq/r²
  • Surface: σ/ε₀
  • Inside: 0
  • Graph peaks at r = R
Portion 3 · Revision flow · Electrostatic Potential and Capacitance
Potential basics
  1. 01Work per unit +ve charge
  2. 02From infinity
  3. 03V = W/q₀
  4. 04Scalar, unit volt
  5. 05Point charge V = kq/r
Dipole potential cases
  1. 01General V = p cos θ / 4πε₀r²
  2. 02Axial θ = 0° → p/4πε₀r²
  3. 03Equatorial θ = 90° → V = 0
  4. 04Dipole V ∝ 1/r²
E and V
  1. 01Move q₀ by dr against E
  2. 02dW = −q₀E dr
  3. 03dV = −E dr
  4. 04E = −dV/dr
  5. 05Field points to falling V
Equipotential properties
  1. 01W = 0 on surface
  2. 02E ⊥ surface
  3. 03Close surfaces = strong field
  4. 04Never intersect
Conductor rules
  1. 01E inside = 0
  2. 02E ⊥ surface outside
  3. 03Charge inside = 0
  4. 04Charge on outer surface
  5. 05V constant
Dielectric chain
  1. 01Apply E₀
  2. 02Polarization → Ep
  3. 03E = E₀ − Ep
  4. 04K = E₀/E
  5. 05K = 1 + χₑ
Capacitor formulas
  1. 01C = q/V
  2. 02Sphere C = 4πε₀r
  3. 03Plates C = Aε₀/d
  4. 04Dielectric slab C = Aε₀/(d − t + t/K)
  5. 05Conducting slab C = Aε₀/(d − t)
Slab cases
  1. 01t = d → KC₀
  2. 02t = d/2 → 2KC₀/(K+1)
  3. 03t = 2d/3 → 3KC₀/(K+2)
Series vs parallel
  1. 01Series: same q, V divides
  2. 021/Cs = 1/C₁ + 1/C₂ + …
  3. 03Parallel: same V, q divides
  4. 04Cp = C₁ + C₂ + …
Energy with dielectric
  1. 01U = ½CV² = Q²/2C
  2. 02Battery OFF: Q const → U₀/K
  3. 03Battery ON: V const → KU₀
  4. 04u = ½ε₀E²
Suggestions · Missing points · Electrostatic Potential and Capacitance
Q1. Define electric potential. Derive the expression for potential due to a point charge.
  • Missing: Common mistake
Q2. Define electric potential difference and one volt.
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q3. Write the potential due to a system of point charges (superposition).
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Quick revision points
Q4. Define electrostatic potential energy and electron volt.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q5. What is potential gradient?
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q6. Differentiate between conductors, insulators and dielectrics. What are polar and non-polar dielectrics?
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q7. Define capacitor, capacitance, permittivity and dielectric constant.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q8. Formula and units sheet — Chapter 2
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q10. Compare electric potential due to an isolated charge and an electric dipole.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q11. Prove that electric field intensity is the negative potential gradient: E = −dV/dr.
  • Missing: Exam tip
  • Missing: Common mistake
Q12. What is an equipotential surface? Write its properties.
  • Missing: 🧠 Remember box
  • Missing: Common mistake
Q13. Derive the potential energy of a system of two and three point charges.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
Q14. Explain the behaviour of conductors in an electric field. What is electrostatic shielding?
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
Q15. Explain dielectrics and polarization. Define dielectric constant, polarization vector, susceptibility and dielectric strength. Prove K = 1 + χₑ.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
  • Missing: Common mistake
Q16. Define electrical capacitance. Find the capacitance of an isolated spherical conductor. Is a 1 F conductor possible?
  • Missing: Exam tip
  • Missing: Common mistake
  • Missing: Quick revision points
Q17. Parallel plate capacitor: principle, capacitance, with dielectric slab and with conducting slab.
  • Missing: 🧠 Remember box
Q18. Derive the equivalent capacitance for series and parallel combination of capacitors.
  • Missing: Exam tip
  • Missing: Common mistake
Q19. Derive the energy stored in a capacitor and energy density. Explain the effect of a dielectric on energy stored.
  • Missing: 🧠 Remember box
  • Missing: Exam tip
Quick facts · Electrostatic Potential and Capacitance
ε₀
8.854 × 10⁻¹² C² N⁻¹ m⁻²
1/4πε₀
9 × 10⁹ N m² C⁻²
1 eV
1.6 × 10⁻¹⁹ J
Unit of potential
Volt = J C⁻¹, [ML²T⁻³A⁻¹]
Unit of capacitance
Farad = C V⁻¹, [M⁻¹L⁻²T⁴A²]
1 µF / 1 nF / 1 pF
10⁻⁶ F / 10⁻⁹ F / 10⁻¹² F
Capacitance of Earth
≈ 711 µF
Energy density
u = ½ε₀E², J m⁻³
One-minute recaps
Q1. Define electric potential. Derive the expression for potential due to a point charge.
  • V = W/q₀
  • Scalar, volt
  • [ML²T⁻³A⁻¹]
  • Point charge V = kq/r
Q9. Electric potential due to an electric dipole — axial line, equatorial line and any point.
  • V_axial = p/4πε₀(r² − l²)
  • Short dipole → p/4πε₀r²
  • V_equatorial = 0
  • V = p cos θ/4πε₀r²
Q11. Prove that electric field intensity is the negative potential gradient: E = −dV/dr.
  • dW = −q₀E dr
  • dV = dW/q₀
  • E = −dV/dr
Q12. What is an equipotential surface? Write its properties.
  • W = 0
  • E ⊥ surface
  • Closer = stronger field
  • Never intersect
Q13. Derive the potential energy of a system of two and three point charges.
  • U(2) = kq₁q₂/r₁₂
  • U(3) = k[q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃]
  • 1 J = 1 C V
Q14. Explain the behaviour of conductors in an electric field. What is electrostatic shielding?
  • E inside = 0
  • E ⊥ surface
  • q inside = 0
  • Charge on outer surface
  • V constant
  • Shielding: car in lightning
Q15. Explain dielectrics and polarization. Define dielectric constant, polarization vector, susceptibility and dielectric strength. Prove K = 1 + χₑ.
  • E = E₀ − Ep
  • K = E₀/E > 1
  • P = np = σp
  • P = χₑε₀E
  • K = 1 + χₑ
Q17. Parallel plate capacitor: principle, capacitance, with dielectric slab and with conducting slab.
  • C = Aε₀/d
  • Dielectric: C = Aε₀/(d − t + t/K)
  • t = d → KC₀
  • Conducting slab: C = Aε₀/(d − t)
Q18. Derive the equivalent capacitance for series and parallel combination of capacitors.
  • Series: same q, 1/Cs = Σ1/C
  • Parallel: same V, Cp = ΣC
  • Cp > largest C, Cs < smallest C
Q19. Derive the energy stored in a capacitor and energy density. Explain the effect of a dielectric on energy stored.
  • U = Q²/2C = ½CV² = ½QV
  • u = ½ε₀E²
  • Battery off → U₀/K
  • Battery on → KU₀