Waves, Fields, and Electromagnetism

Posted on Dec 2, 2024 in Physics

  • Waves: Disturbances in Space
  • A wave is a disturbance that propagates through space, carrying energy and momentum without displacing matter.
  • Longitudinal vs. Transverse Waves
  • Longitudinal waves: Propagation direction is parallel to vibration direction. Example: Sound waves.
  • Transverse waves: Propagation direction is perpendicular to vibration direction. Example: Electromagnetic waves, S-waves (Seismic).

Similarities and Differences Between Electric and Gravitational Fields

Analogies

  • Both fields are central fields created by a point source (mass or charge).
  • Field lines are open and radially symmetric.
  • Both are conservative fields with potential energy.
  • Field strength is directly proportional to the source and inversely proportional to the square of the distance.

Differences

  • Electric forces can be attractive or repulsive, while gravitational forces are always attractive.
  • Electric field lines originate from positive charges and end on negative charges. Gravitational field lines always end on masses.
  • The electric constant (k) depends on the medium, while the gravitational constant (G) is universal.
  • Electric forces are much stronger at the microscopic level.
  • At the macroscopic level, electric forces often cancel out, making gravitational forces dominant.

Representation of the Electric Field

  • Field lines: Tangent to the electric field vector at each point. Density is proportional to field strength. Originate from positive charges and end on negative charges.
  • Equipotential surfaces: Connect points with the same electric potential. Perpendicular to field lines. Work done by the field on a charge moving on an equipotential surface is zero. For a point charge, equipotential surfaces are concentric spheres.

Gravitational Interaction: Newton’s Law of Universal Gravitation

Two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Kepler’s Laws of Planetary Motion

  1. Planets move in elliptical orbits with the Sun at one focus.
  2. The line joining a planet and the Sun sweeps out equal areas in equal times.
  3. The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun.

Coulomb’s Law

The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. (Valid for stationary point charges).

Electric Field

A disturbance produced by a charged body in the surrounding space. A static charge produces an electrostatic field. Described by electric field strength (vector) and electric potential (scalar).

Huygens’ Principle

Every point on a wavefront acts as a source of secondary wavelets, propagating with the same speed and frequency as the original wave. The envelope of these wavelets forms the new wavefront.

Diffraction, Reflection, and Refraction

  • Diffraction: Bending of waves around obstacles or through openings comparable in size to the wavelength.
  • Reflection: Bouncing of a wave off a boundary between two media.
    • Laws of Reflection:
      1. Incident ray, normal, and reflected ray are coplanar.
      2. Angle of incidence equals angle of reflection.
  • Refraction: Change in direction of a wave as it passes from one medium to another.
    • Laws of Refraction:
      1. Incident ray, normal, and refracted ray are coplanar.
      2. Snell’s Law: n1sinθ1 = n2sinθ2 2Q ==

Wave Interference

Superposition of two or more waves in the same medium. Governed by the superposition principle: The resultant displacement is the sum of individual displacements.

  • Constructive interference: Resultant amplitude is greater than individual amplitudes.
  • Destructive interference: Resultant amplitude is less than individual amplitudes.

Representation of the Gravitational Field

  • Field lines: Tangent to the gravitational field vector. Density is proportional to field strength.
  • Equipotential surfaces: Connect points with the same gravitational potential. Perpendicular to field lines. Work done by gravity on a mass moving on an equipotential surface is zero. For a point mass, equipotential surfaces are concentric spheres.

Properties of Electric Charge

  • Conservation: Total charge remains constant.
  • Quantization: Charge exists in discrete multiples of the elementary charge (electron charge).

Electromagnetic Induction

Production of electric currents by changing magnetic fields. Depends on the variation of magnetic flux (number of field lines passing through a circuit). Basis for devices like transformers and generators.

Faraday’s Law

A changing magnetic flux induces an electromotive force (emf) and current in a circuit.

Lenz’s Law

The induced current creates a magnetic field that opposes the change in flux.

Oersted’s Experiment

An electric current produces a magnetic field, demonstrated by the deflection of a compass needle near a current-carrying wire.