Study Notes on Electrostatics

ELECTRIC CHARGE

• Definition: Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects.
• Concept of Charge: The excess or deficiency of electrons in a body gives rise to the concept of charge.
• Types of Charge:
  • (i) Positive Charge: A deficiency of electrons compared to protons.
  • (ii) Negative Charge: An excess of electrons compared to protons.
• SI Unit of Charge: Coulomb (C).
  • 1 Coulomb is equivalent to $1 ext{ A} imes 1 ext{ s}$.
  • Dimension: [A T]
• Practical Units of Charge:
  • Ampere-hour (3600 C)
  • Faraday (96500 C)
• Quanta of Charge: Millikan calculated the quant of charge using the Highest Common Factor (H.C.F.) method, equal to the charge of an electron:
  • $1 C = 3 imes 10^9$ stat coulombs
  • $1 ext{ Faraday} = 96500 ext{ C}$

SPECIFIC PROPERTIES OF CHARGE

1. Charge is a Scalar Quantity: It represents the excess or deficiency of electrons without directional properties.
2. Charge is Transferable: When a charged body is in contact with another, electrons can transfer from one to the other.
3. Charge is Always Associated with Mass: The presence of charge indicates the existence of mass.
   • Charge can affect the mass of a body:
     • Positive charge causes a decrease in mass.
     • Negative charge causes an increase in mass.
4. Charge is Quantized: All free charges are integral multiples of a basic unit of charge represented by e (the charge of an electron).
   • $q = ne$, where n is an integer.
   • Charge on a proton: $+1.6 imes 10^{-19} ext{ C}$ = Charge on an electron: $-1.6 imes 10^{-19} ext{ C}$
5. Conservation of Charge: The total charge in an isolated system remains constant over time; charge can neither be created nor destroyed.
   • Valid in all types of reactions (chemical/nuclear) with no exceptions.
6. Charge is Invariant: Charge is constant regardless of motion or frame of reference.
7. Accelerated Charge Radiates Energy:
8. Attraction and Repulsion:
   • Similar charges repel each other while opposite charges attract.

METHODS OF CHARGING

1. Charging by Friction: When two bodies are rubbed against each other, electrons move from one body to another based on their work functions.
2. Charging by Induction: Bringing a charged body close to a neutral conductor results in opposite charges being induced in the conductor, leading to redistribution of charge within the conductor.
   • Important Facts:
     • No gain or loss of charge in the inducing body.
     • Nature of induced charge is opposite to that of the inducing charge.
     • Induction occurs only in bodies, not in subatomic particles.
3. Charging by Conduction: Direct contact between a charged and uncharged body facilitates transfer of charge due to contact.
   • Characteristics:
     • Charged body loses charge equal to what the uncharged body gains.
     • Gained charge is always less than the initial charge on the charged body.

Illustrations:

• Illustration 1: When rubbing a piece of polythene with wool, it accumulates a charge of $-2 imes 10^{-7} ext{ C}$. Amount of mass transferred to polythene:
  • $Q = ne$
  • N = rac{Q}{e} = rac{-2 imes 10^{-7}}{1.6 imes 10^{-19}}
    ightarrow n ext{ (number of electrons)}.
  • Mass of transferred electrons = $n imes m_{electron}= 1.25 imes 10^{12} imes 9.1 imes 10^{-31} = 11.38 imes 10^{-19} ext{ kg}$.

COULOMB'S LAW

• Statement: The electrostatic force between two point charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between their centers, expressed as:
  • $F ext{ (force)} imes \frac{1}{r^2}, ext{ where } F ext{ is directly proportional to } q_1 imes q_2$.
• Coulomb's Law in Vector Form:
  • $F_{12} = k \frac{q_1 q_2}{r^2} ext{ along the direction of } extbf{r}$, where r is the unit vector from charge q2 to q1, and k is Coulomb's constant:
  • $k = 9 imes 10^9 N m^2/C^2$.

Important Points about Coulomb's Law:

1. The force acts between stationary point charges in rest.
2. Based on experimental observations, it is universally valid.
3. Analogous to Newton’s law of gravitation.
   • Key differences:
     • Electric forces can be attractive or repulsive, while gravitational forces are only attractive.
     • Electric force magnitude is significantly stronger than gravitational force (e.g. F_E >> F_G).
     • Electric force depends on the medium, while gravitational force does not.
4. Conservation of Energy: Work done in moving a charge around in an electric field is zero for closed paths (conservative force).