Wave Properties, Electric Charge, and Induction

Posted on Dec 17, 2024 in Physics

Wave Classifications

There are several possible classifications of waves.

By Medium of Propagation

Electromagnetic and gravitational waves do not need a material medium to propagate and can, therefore, propagate in a vacuum. Examples of electromagnetic waves are: light, radio waves, television and mobile phones, microwaves, ultraviolet rays, gamma rays, etc.

Mechanical waves need a material medium to propagate. Examples include: sound, water waves, and vibrations of a string. These waves are the result of the orderly movement of many particles.

By Direction of Vibration

Transverse waves: vibration occurs in a direction perpendicular to the direction of propagation. Examples: string and electromagnetic waves, and shock waves.

Longitudinal waves: vibration occurs in the direction of propagation. Example: sound waves.

By Dimensions of Propagation

  • One-dimensional: (vibrations on a string)
  • Two-dimensional: (waves on the surface of a liquid or vibration in a membrane)
  • Three-dimensional: (light and sound)

Huygens’ Principle

Huygens’ principle is a mechanism for constructing wave fronts from previous fronts. A wavefront is a surface that passes through points where a wave oscillates with the same phase.

The principle states that: Points in a wavefront become sources of secondary waves, whose envelope is a new primary wavefront.

To apply it, small circles of radius are plotted with centers at different points on a wavefront, and then the envelope of the circles is plotted, which is the new wavefront.

A consequence of Huygens’ principle is that all rays take the same time between two consecutive wave fronts. Rays are lines perpendicular to the wave fronts and correspond to the line of wave propagation.

Although Huygens formulated it for matter waves, its principle is valid for all types of waves. Kirchhoff extended the method to electromagnetic waves.

Electric Charge and Coulomb’s Law

Electric charge is a property of matter responsible for electromagnetic interaction. It has the following properties:

  • It may be positive or negative.
  • The total charge of a group of particles is the sum with the sign of their individual charges.
  • The total electric charge of an isolated system is conserved.
  • The charge is quantized: it only comes in discrete amounts that are multiples of a basic amount: |e| = 1.6 ยท 10-19 C. The electron charge is -|e| and the proton charge is +|e|.

The charge unit in SI is the coulomb.

Coulomb’s law describes the interaction between electric charges at rest. The law states: The force exerted by a point charge on another is proportional to the product of the charges and inversely proportional to the square of the distance that separates them. It is a central force directed along the line connecting the charges. It is repulsive if the charges have the same sign and attractive if they have opposite signs.

Mathematically: F = K * (q1 * q2) / r2 * ur, where ur is the unit vector that goes from q1 to q2. The constant of proportionality is called the Coulomb constant and its value is: K = 9.109 N m2 / C2. In other media than vacuum, the constant takes different values.

The charge q2 exerts on q1 a force equal but opposite to the force that q1 exerts on q2. Electrostatic forces comply with the principle of superposition: the net force exerted by a set of charges on another is the vector sum of all forces exerted upon it.

Electromagnetic Induction

Electromagnetic induction is a phenomenon where, under certain conditions, electricity is produced with magnetism. Scientists like Faraday and Henry observed that an electrical current is generated in a circuit in the following circumstances:

  • If a magnet moves towards or away from the circuit. Or if the circuit moves relative to the magnet.
  • If there is relative motion between the circuit and another circuit carrying a continuous current.
  • If the second circuit carries a variable current, even if both are stationary.
  • If the circuit is deformed within a magnetic field.

All the above facts can be explained by Faraday’s law, which states that the temporal variation of magnetic field flow through a circuit generates an electromotive force (EMF):

The EMF is the work per unit of charge being carried on the circuit. It is measured in volts in the SI.