class 12 notes

Class 12 Physics Notes Chapter 1 (Electric charges and fields) – Physics Part-I Book

Philoid

Philoid

— 8 min read

Physics Part-I
Alright class, let's begin our focused revision of Chapter 1: Electric Charges and Fields. This is a fundamental chapter, and understanding these concepts well is crucial for many government exams containing a physics section. Pay close attention to the definitions, laws, formulas, and their applications.

Chapter 1: Electric Charges and Fields - Detailed Notes

1. Electric Charge

  • Definition: An intrinsic property of elementary particles of matter which gives rise to electric force between various objects.
  • Types: Positive (+) and Negative (-). Like charges repel, unlike charges attract.
  • Scalar Quantity: Charge is a scalar quantity.
  • SI Unit: Coulomb (C).
  • Elementary Charge (e): The smallest unit of free charge known in nature. Charge on an electron = -e, charge on a proton = +e. e = 1.602 × 10⁻¹⁹ C.
  • Properties of Electric Charge:
    • Additivity: The total charge of a system is the algebraic sum (considering signs) of all individual charges in the system. Q_total = q₁ + q₂ + q₃ + ...
    • Conservation: The total charge of an isolated system remains constant. Charge can neither be created nor destroyed, only transferred from one body to another.
    • Quantization: Charge on any body is always an integral multiple of the elementary charge 'e'. Q = ne, where 'n' is an integer (n = ±1, ±2, ±3, ...) and 'e' is the elementary charge.

2. Methods of Charging

  • Charging by Friction (Triboelectric charging): Rubbing two suitable materials transfers electrons from one material (which becomes positively charged) to the other (which becomes negatively charged).
  • Charging by Conduction: Charging an uncharged conductor by bringing it into direct contact with a charged conductor. The charge is shared between the two conductors.
  • Charging by Induction: Charging a conductor without direct contact. A charged body brought near an uncharged conductor causes charge separation (polarization) in the conductor. By grounding the conductor momentarily, it can acquire a net charge opposite to that of the inducing body.

3. Coulomb's Law

  • Statement: The electrostatic force of attraction or repulsion between two stationary point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
  • Scalar Form: F = k |q₁q₂| / r²
    • F = magnitude of the force
    • q₁, q₂ = magnitudes of the point charges
    • r = distance between the charges
    • k = Electrostatic force constant or Coulomb's constant. k = 1 / (4πε₀) ≈ 9 × 10⁹ Nm²/C² in vacuum/air.
    • ε₀ = Permittivity of free space = 8.854 × 10⁻¹² C²/Nm². Its dimensional formula is [M⁻¹ L⁻³ T⁴ A²].
  • Effect of Medium: If charges are placed in a medium with relative permittivity εᵣ (or dielectric constant K), the force becomes F_medium = F_vacuum / εᵣ = F_vacuum / K.
  • Vector Form: Describes both magnitude and direction. The force on q₂ due to q₁ is F₂₁ = k (q₁q₂) / r₂₁² * r̂₂₁, where r̂₂₁ is the unit vector pointing from q₁ to q₂. Similarly, F₁₂ = k (q₁q₂) / r₁₂² * r̂₁₂. Note: F₂₁ = -F₁₂ (obeys Newton's third law).
  • Principle of Superposition: The total force on any given charge due to a number of other charges is the vector sum of the individual forces exerted on the given charge by all other charges. F_total = F₁ + F₂ + F₃ + ...

4. Electric Field (E)

  • Concept: The region around a charged body within which its electric influence can be experienced by another charge.
  • Electric Field Intensity (E): The electric force experienced per unit positive test charge placed at that point, without disturbing the source charge. E = F / q₀ (where q₀ is a small positive test charge).
  • SI Unit: Newton per Coulomb (N/C) or Volt per meter (V/m).
  • Dimensional Formula: [M L T⁻³ A⁻¹].
  • Vector Quantity: Direction is the direction of force on a positive test charge.
  • Electric Field due to a Point Charge (q): E = k q / r² * r̂ (where r̂ is the unit vector pointing from the source charge q to the point). Direction is radially outward for +q and radially inward for -q.
  • Principle of Superposition for Electric Fields: The total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge at that point. E_total = E₁ + E₂ + E₃ + ...

5. Electric Field Lines

  • Definition: Imaginary lines or curves drawn in an electric field such that the tangent at any point gives the direction of the electric field intensity at that point.
  • Properties:
    • Originate from positive charges and terminate on negative charges.
    • Tangent at any point gives the direction of the electric field E at that point.
    • They never intersect each other (because E has a unique direction at any point).
    • They are continuous curves in a charge-free region.
    • The density of field lines (number of lines per unit area perpendicular to the lines) represents the magnitude of the electric field. Closer lines mean stronger field.
    • They are always perpendicular to the surface of a conductor (in electrostatic equilibrium).
    • They do not form closed loops (electrostatic field is conservative).
    • Field lines tend to contract longitudinally (explaining attraction) and exert lateral pressure (explaining repulsion).

6. Electric Dipole

  • Definition: A system of two equal and opposite point charges (+q and -q) separated by a small finite distance (usually denoted by 2a).
  • Electric Dipole Moment (p): A vector quantity measuring the strength of the dipole.
    • Magnitude: p = q × (2a)
    • Direction: From the negative charge (-q) to the positive charge (+q).
    • SI Unit: Coulomb-meter (C m).
  • Electric Field due to a Dipole:
    • On the Axial Line: (Point lies on the line joining the two charges)
      E_axial = (1 / 4πε₀) * (2pr / (r² - a²)²)
      For r >> a (short dipole): E_axial ≈ (1 / 4πε₀) * (2p / r³) (Direction along p)
    • On the Equatorial Line: (Point lies on the perpendicular bisector)
      E_equatorial = (1 / 4πε₀) * (p / (r² + a²)^(3/2))
      For r >> a (short dipole): E_equatorial ≈ (1 / 4πε₀) * (p / r³) (Direction opposite to p)
    • Note: For a short dipole at the same distance r, |E_axial| = 2 |E_equatorial|.
  • Torque on a Dipole in a Uniform Electric Field (E):
    • τ = pE sinθ, where θ is the angle between p and E.
    • Vector form: τ = p × E.
    • Torque is maximum when θ = 90° (τ_max = pE) and minimum (zero) when θ = 0° or 180°.
  • Potential Energy of a Dipole in a Uniform Electric Field (E):
    • U = -pE cosθ = -p . E
    • Minimum potential energy (most stable equilibrium) when θ = 0° (U = -pE).
    • Maximum potential energy (most unstable equilibrium) when θ = 180° (U = +pE).
    • Zero potential energy when θ = 90°.

7. Electric Flux (Φ)

  • Concept: A measure of the total number of electric field lines passing normally through a given area.
  • Definition: For a uniform electric field E and a plane area A, the electric flux is Φ = E . A = EA cosθ, where θ is the angle between the electric field vector E and the area vector A (vector normal to the surface).
  • Scalar Quantity.
  • SI Unit: Newton meter squared per Coulomb (Nm²/C) or Volt-meter (Vm).
  • Dimensional Formula: [M L³ T⁻³ A⁻¹].

8. Gauss's Law

  • Statement: The total electric flux (Φ) through any closed surface (also called a Gaussian surface) is equal to 1/ε₀ times the net charge (q_enclosed) enclosed by the surface.
  • Mathematical Form: Φ_total = ∮ E . dA = q_enclosed / ε₀
  • Key Points:
    • Applies to any closed surface of any shape.
    • The charge q_enclosed is the algebraic sum of all charges inside the closed surface. Charges outside do not contribute to the net flux.
    • Crucial for calculating electric fields for symmetric charge distributions where direct application of Coulomb's law is difficult.
    • Gaussian surface is an imaginary closed surface chosen conveniently (usually exploiting symmetry) to apply the law.

9. Applications of Gauss's Law

  • Electric Field due to an Infinitely Long Straight Uniformly Charged Wire:
    • Charge per unit length (Linear charge density) = λ.
    • Gaussian surface: Cylinder of radius r and length l, coaxial with the wire.
    • Electric Field: E = λ / (2πε₀r). E is proportional to 1/r.
  • Electric Field due to a Uniformly Charged Infinite Plane Sheet:
    • Charge per unit area (Surface charge density) = σ.
    • Gaussian surface: Cylinder cutting through the sheet.
    • Electric Field: E = σ / (2ε₀). E is uniform and independent of the distance from the sheet.
  • Electric Field due to a Uniformly Charged Thin Spherical Shell (Radius R, Total Charge Q):
    • Charge per unit area σ = Q / (4πR²).
    • Outside the shell (r > R): E = (1 / 4πε₀) * (Q / r²). The shell behaves like a point charge Q located at its center.
    • On the surface of the shell (r = R): E = (1 / 4πε₀) * (Q / R²).
    • Inside the shell (r < R): E = 0. The electric field inside a uniformly charged thin spherical shell is zero.

10. Continuous Charge Distribution

  • When charge is distributed continuously over a line, surface, or volume.
  • Linear Charge Density (λ): Charge per unit length. λ = dq / dl. SI Unit: C/m.
  • Surface Charge Density (σ): Charge per unit area. σ = dq / dA. SI Unit: C/m².
  • Volume Charge Density (ρ): Charge per unit volume. ρ = dq / dV. SI Unit: C/m³.

Multiple Choice Questions (MCQs)

  1. The property of electric charge that ensures the total charge in an isolated system remains unchanged is called:
    a) Quantization of charge
    b) Additivity of charge
    c) Conservation of charge
    d) Induction of charge

  2. Two point charges +q and +4q are separated by a distance 'r'. Where should a third charge Q be placed on the line joining them so that it is in equilibrium?
    a) At r/3 from +q
    b) At r/2 from +q
    c) At 2r/3 from +q
    d) At r/4 from +q

  3. The SI unit of permittivity of free space (ε₀) is:
    a) C² N⁻¹ m⁻²
    b) N m² C⁻²
    c) C N⁻¹ m⁻²
    d) N m C⁻²

  4. Which of the following statements about electric field lines is incorrect?
    a) They originate from positive charges.
    b) They can form closed loops.
    c) They never intersect each other.
    d) The tangent at any point gives the direction of the electric field.

  5. An electric dipole is placed in a uniform external electric field E. The net electric force on the dipole is:
    a) pE
    b) 2pE
    c) Zero
    d) Dependent on the orientation

  6. The electric field inside a uniformly charged thin spherical shell is:
    a) σ / ε₀
    b) σ / 2ε₀
    c) Zero
    d) Q / (4πε₀r²)

  7. Gauss's law is useful for calculating the electric field when the charge distribution is:
    a) Random
    b) Symmetric
    c) Only for point charges
    d) Only for dipoles

  8. What is the electric flux through a closed surface enclosing an electric dipole?
    a) q / ε₀
    b) 2q / ε₀
    c) -q / ε₀
    d) Zero

  9. When a glass rod is rubbed with silk, the glass rod acquires a positive charge because:
    a) Protons are transferred from silk to glass.
    b) Electrons are transferred from glass to silk.
    c) Protons are transferred from glass to silk.
    d) Electrons are transferred from silk to glass.

  10. The electric field due to an infinitely long straight uniformly charged wire at a distance 'r' is proportional to:
    a) r
    b) 1/r
    c) 1/r²
    d) r²

Answers to MCQs:

  1. (c) Conservation of charge
  2. (a) At r/3 from +q (Let the distance from +q be x. Force due to +q = k(qQ)/x². Force due to +4q = k(4qQ)/(r-x)². For equilibrium, these forces must be equal: k(qQ)/x² = k(4qQ)/(r-x)². Solving gives (r-x)² = 4x², so r-x = 2x, which leads to x = r/3.)
  3. (a) C² N⁻¹ m⁻² (From F = (1/4πε₀) q₁q₂/r², ε₀ = q₁q₂ / (4πFr²). Unit = C² / (N m²) )
  4. (b) They can form closed loops (Electrostatic field lines do not form closed loops).
  5. (c) Zero (The forces on +q and -q due to the uniform field are equal and opposite, resulting in zero net force).
  6. (c) Zero (According to Gauss's law application).
  7. (b) Symmetric
  8. (d) Zero (The net charge enclosed by the surface is +q + (-q) = 0).
  9. (b) Electrons are transferred from glass to silk.
  10. (b) 1/r (E = λ / (2πε₀r)).

Study these notes thoroughly. Remember to practice numerical problems based on Coulomb's law, electric field calculations, dipole moments, and Gauss's law applications. Good luck with your preparation!

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