Electrostatics Study Notes

ELECTROSTATICS - I

1. Electrostatic Force

  • Electrostatic Force involves the interaction between static electric charges.

2. Frictional Electricity

  • Definition: Frictional electricity is generated by rubbing two suitable materials together, causing a transfer of electrons.

  • Example:

    • When glass and silk are rubbed together, electrons from the glass, which are more loosely bound, move to the silk.
    • Result: Glass becomes positively charged (+) and silk becomes negatively charged (−).
    • When ebonite and fur are rubbed together, the loosely bound electrons from the fur transfer to the ebonite.
    • Result: Ebonite becomes negatively charged (−) and fur becomes positively charged (+).

  • Key Note:

    • Electrification (positive or negative) results from electron transfer:
    • If electrons are lost, the body becomes positively charged.
    • If electrons are gained, the body becomes negatively charged.

  • Charge Assignment Rule:

    • The body appearing early in the list becomes positively charged, while the later one becomes negatively charged when rubbed together:

Charge Assignments:

Column I (+ve Charge)Column II (-ve Charge)
GlassSilk
Wool, FlannelAmber, Ebonite, Rubber, Plastic
EbonitePolythene
Dry hairComb

3. Properties of Electric Charges

  1. Types of Charges: Two fundamental types exist - positive and negative.
  2. Charge Interactions: Like charges repel each other, while unlike charges attract each other.
  3. Nature of Charge: Charge is a scalar quantity.
  4. Additivity of Charge: Charges are additive in nature:
    • Example: +2 ext{ C} + 5 ext{ C} - 3 ext{ C} = +4 ext{ C}
  5. Quantization of Charge:
    • Electric charge exists in discrete packets (quantized) expressed in multiples of the fundamental electronic charge (e = 1.6 imes 10^{-19} ext{ C}).
    • Formula: q = oldsymbol{ ext{±}} ne where n is an integer (1, 2, 3, …).
  6. Conservation of Charge:
    • The total charge is conserved; the sum of positive and negative charges in an isolated system remains constant.
    • Example: In charging a glass rod with silk, equal but opposite charges appear, maintaining a net charge of zero before and after rubbing.
  • Discussion: The principle holds true irrespective of the system's velocity.

4. Recent Developments

  • Existence of quarks with fractional charges rac{1}{3} e and rac{2}{3} e has been postulated.
    • If detected, it will redefine the minimum charge quantum, while fundamental quantization laws remain valid.

5. Coulomb's Law

  • Definition: Coulomb's Law describes the force between two point charges. It states that:

    • The electrostatic force (attraction or repulsion) is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

  • Mathematical Statement:

    • F ext{ } oldsymbol{ ext{α}} rac{q1 q2}{r^2}
    • Force can be expressed as:
    • F = k rac{q1 q2}{r^2} where k is the electrostatic force constant (Coulomb's constant).

  • Constant in Vacuum:

    • k = rac{1}{4 ext{π} ext{ε}0} where ext{ε}0 is the permittivity of free space.

  • In Medium:

    • k = rac{1}{4 ext{π} ext{ε}} where ε is the dielectric medium's absolute permittivity.

  • Force Calculation:

    • In medium, F = rac{q1 q2}{r^2} imes rac{1}{4 ext{π} ext{ε}0 ext{ε}r} where ext{ε}_r is the dielectric constant.

  • Values of ε0:

    • ext{ε}_0 = 8.8542 imes 10^{-12} ext{C}^2 ext{N}^{-1} ext{m}^{-2}
    • k = 9 imes 10^9 ext{N} ext{m}^2 ext{C}^{-2}.

6. Coulomb's Law in Vector Form

  • Coulomb's Law can be expressed using vectors:
    • extbf{r} = extbf{F21} = extbf{F12} = rac{q1 q2 extbf{r{12}}}{4 ext{π} ext{ε}0 r^2}.
  • For charges with the same sign (q1 q2 > 0):
    • F{12} ext{ } oldsymbol{ ext{α}} rac{q1 q_2}{r^2} with unity vectors in the same direction.
  • For opposite charges (q1 q2 < 0):
    • F{12} = -F{21} indicates attraction.

7. Units of Charge

  • SI Unit: The unit of electric charge is the coulomb (C).
  • Definition: One coulomb is the charge that, when placed at a distance of one meter from an equal charge at rest in a vacuum, repels it with a force of 9 imes 10^9 ext{ N}.

8. Relative Permittivity or Dielectric Constant

  • Definition: The dielectric constant (relative permittivity, specific inductive capacity) is the ratio of the absolute permittivity of a medium (ε) to that of free space ( ext{ε}_0).
    • Formula: K = rac{ ext{ε}}{ ext{ε}_0}.
  • Force Comparison: It can also be defined as the ratio of electrostatic forces:
    • K = rac{Fv}{Fm} where Fv is the force in vacuum and Fm is the force in the medium.
  • Note on Units: The dielectric constant is dimensionless (no unit).

9. Continuous Charge Distribution

  • Definition: Charge distributions that cover a volume with much smaller dimensions than the distance from an observation point can be viewed as point charges.
  • Density Consideration: Just as density is applied in solids, liquids, and gases, charge distributions likewise have density.

i) Linear Charge Density (λ)

  • Definition: Charge distributed along a line (e.g., circumference of a circle).
  • Expression:
    • ext{Linear charge density} ext{ λ} = rac{dq}{dl}
    • SI unit: C/m.
    • Total charge over length:
    • q = ext{∫} λ ext{ } dl

ii) Surface Charge Density (σ)

  • Definition: Charge distributed over a surface area.
  • Expression:
    • ext{Surface charge density} ext{ σ} = rac{dq}{dS}
    • SI unit: C/m².
    • Total charge over surface area:
    • q = ext{∫} σ ext{ } dS

iii) Volume Charge Density (ρ)

  • Definition: Charge distributed throughout a volume.
  • Expression:
    • ext{Volume charge density} ext{ ρ} = rac{dq}{dV}
    • SI unit: C/m³.
    • Total charge over volume:
    • q = ext{∫} ρ ext{ } dV

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