Maxwell’s Equations

Learn.

Maxwell developed and derived four equations, his contribution to classical electromagnetism was showing the interrelatedness of phenomena which were thought to be separate. For HSC level, we recommend knowing each of the four laws qualitivly.

Maxwell’s 4 laws to develop a unified theory of classical electromagnetism are:

  • Gauss’s Law of Electrical Flux – Electrical fields radiate out from a point charge – leaving it. A gaussian surface is smooth and encloses a charge
  • Gauss’s Law of Magnetic Flux – Since all magnetic field lines are looped so they enter and re-enter an object, there are no magnetic monopoles
  • Faraday’s Law of Electromagnetic Induction – Changing magnetic fields generate changing electric field
  • Ampere’s Circuital Law – changing electric field generates a chang in magnetic fluxperpendicular to the plane (vice versa of Faraday’s law) of the electric field (using the displacement current). The constants μ0 and ε0 can be measured in laboratory and are related to this.

Master.

Question 1. [5 marks]

Evaluate the significance of Maxwell’s equations to the field of classical electromagnetism.

Answers.

Maxwell provided equations, allowing for the unification of scientific understandings related to electromagnetism (EM). This increased our understanding of EM and allowed us improved our ability to apply these concepts.

  • Gauss’s Law of Electrical Flux – Electrical fields radiate out from a point charge – leaving it. A gaussian surface is smooth and encloses a charge
    • Predict how electric point chares interact with one another, used in cathode ray tubes – a technology employed in old fashioned TVs.
  • Gauss’s Law of Magnetic Flux – Since all magnetic field lines are looped so they enter and re-enter an object, there are no magnetic monopoles
    • Understanding of splitting a bar magnet creates two new bar magnet, both with a North and South field. This can be applied to commercial magnetic creation.
  • Faraday’s Law of Electromagnetic Induction – Changing magnetic flux generate changing electric field
    • Applied to the concept of a generator.
  • Ampere’s Circuital Law – changing electric field generates a changing magnetic field perpendicular to the plane (vice versa of Faraday’s law) of the electric field (using the displacement current). The constants μ0 and ε0 can be measured in laboratory and are related to this.
    • Applied to the concept of a motor.
GuidelinesMarks
A rough explanation of each of the four equations, linking to who’s law it is, and link to the argument.1 each (total of 4)
Provides a valid argument to the question1

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