Lecture Notes: Professor Ramamurti Shankar - Atomic Structure and Electric Forces

Summary of Last Lecture

• Atomic Structure

  • Everything is made of atoms.
  • An atom consists of a nucleus (protons and neutrons) and electrons.

• Electric Charge

  • Entities have a property called electric charge (symbol: q).

  • Charge values:

    • Neutron: q = 0
    • Electron: q = -1.6 x 10^-19 C
    • Proton: q = +1.6 x 10^-19 C

  • Electric charge interacts through Coulomb's law:

    • Force between two charges:

      F = (q1 * q2) / (4πε₀r²)

  • Similar Sign Charges: Repulsive

  • Opposite Sign Charges: Attractive*

Key Concepts

• Superposition Principle

  • For multiple charges, the net force on a charge is the vector sum of individual forces from all other charges.
  • Superposition is an experimental fact for classical electromagnetic theory.

• Comparison of Forces

  • Gravitational force is much weaker than electric force (approximately 10^-40 times weaker).
  • The strong nuclear force, which holds protons together, is stronger than electric force.

• Nuclear Forces

  • Protons repel due to electric charge, yet are held together in the nucleus by the strong nuclear force.
  • Neutrons play a crucial role in adding stability to the nucleus without increasing electrical repulsion.

• Coulomb’s Law

  • Important for solving problems related to electric forces, focusing on interactions between two charges.

Electric Field Concept

• Electric Field (E)

  • Defined as the force per unit charge experienced by a charge placed in the field.

  • The electric field can exist independently of charges, defined everywhere in space.

  • Formula for the electric field due to a charge Q:

    E = (Q / (4πε₀r²)) * r̂

• Graphical Representation of Electric Fields

  • Field lines visualize the strength and direction of the electric field.
  • Densely packed lines indicate a stronger electric field.
  • Electric field direction: From positive to negative charges.*

Dipole Moment

• Dipole Configuration

  • A dipole consists of two equal and opposite charges.

  • The dipole moment (P) is defined as:

    P = Q * d

    where d is the distance between the two charges.

• Electric Field of a Dipole

  • Electric field due to a dipole falls off as 1/r³, when far from the dipole.

• Torque on a Dipole in an Electric Field

  • The torque (τ) experienced by a dipole in an electric field is given by:

    τ = P x E

  • The dipole will align itself with the electric field, leading to potential energy associated with its orientation:

    U = -P • E*

Conclusion

• Move away from thinking of direct charge interactions to understanding electric fields produced by charges and how they interact with other charges in the field.
• Review important equations for electric field and dipole moment as they will be critical for problem-solving in future discussions.