Coulomb's Law and Charge Concepts

UNIT-ELECTROSTATICS

L-1 COULOMB'S LAW

  • Definition of Atom:

    • An atom is electrically neutral, meaning the number of protons equals the number of electrons.

    • The charge of an electron is represented as -e = -1.6 imes 10^{-19} C.

    • The mass of an electron m_e is approximately 9.1 imes 10^{-31} kg.

    • The charge of a proton is represented as +e = +1.6 imes 10^{-19} C.

    • The mass of a proton mp is approximately 1.66 imes 10^{-27} kg and the mass ratio is mp ext{ (proton)} : m_e = 1836 : 1.

  • Atomic Structure of Sodium (Na):

    • Atomic Number (Z) = 11 (number of protons).

    • Mass Number (A) = 23 (number of protons + neutrons).

    • Electron configuration: Na atom has 11 electrons arranged as 1s^2 2s^2 2p^6 3s^1.

Concepts of Charge

  • Charge transfer occurs through:

    • Materials that allow charge movement (conductors).

    • The quantization of charge, where q = ext{n} e (with n as an integer). Each charge is a multiple of the elementary charge.

    • Transfer occurs when charges interact with like and unlike charges.

  • Charging Methods:

    • By Friction: Rubbing surfaces transfer electrons. Example: Glass rubbed with silk becomes positive, rubber with wool becomes negative.

    • By Conduction: Direct contact between charged and neutral bodies allows charge to spread evenly.

    • By Induction: Bringing a charged object near a neutral one redistributes its charge.

Coulomb's Law

  • Formula:

    • F = k \frac{Q1 Q2}{r^2} where

    • F is the force between two charges,

    • k is Coulomb's constant (9 \times 10^9 \ \text{N m}^2/C^2),

    • Q1 and Q2 are the magnitudes of the charges,

    • r is the distance between the centers of the two charges.

  • Properties:

    • The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

    • Forces between charges are equal in magnitude and opposite in direction (Newton's Third Law).

Properties of Electric Charge

  1. Transferability: Charge can move between bodies.

  2. Mass Association: Charge is associated with mass.

  3. Conservation: Charge cannot be created or destroyed.

  4. Invariance: The value of the elementary charge remains constant regardless of the particle's speed.

  5. Field Production: Charge results in electric and magnetic fields and can radiate energy when accelerated.

Quantization of Charge

  • Charge can take discrete values based on integers multiples of the elementary charge (e):

    • Q = ext{n}e, where n = 1, 2, 3…

Comparison of Charge and Mass

  • Charge: Can be positive, negative, or zero, does not depend on velocity, and is always conserved. The force can be attractive or repulsive.

  • Mass: Always positive, increases with velocity, potentially non-conserved, and always attracts with gravitational force.

Summary on Charge Interactions

  • When similar charges come together, they repel each other; opposite charges attract.

  • Uniformly charged conductors have charges distributed on their surface.

  • Charge distribution varies on irregular shapes, notably near sharp points.

  • Questions and Examples:

    • If a charge is transferred, it can take the form of electrons and can be quantified as integer multiples of the elementary charge.

  • Also, practical applications of Coulomb's Law in predicting forces between particles (e.g., electrostatics in devices and natural phenomena).

Example Calculations

  • Force Calculation: Calculate the force between two charges, 3C and 4C, placed 2m apart:

    • F = 9 \times 10^9 \frac{(3)(4)}{(2^2)} = 54 \times 10^9 \text{N}.

End of Notes