Maxwell Equation Teardown

Definition

 Maxwell's equations form the fundamental principles governing electromagnetism.

• Gauss's Law:

  • Electric field emanates either inward or outward from a charge.

  • The sum of electric field lines cutting through any enclosed imaginary sphere is equal to the electric charge.

• Gauss's Law for Magnetism:

  • Magnetic field forms a closed loop around a current-carrying wire or magnet.

  • The sum of magnetic field lines cutting through any enclosed imaginary sphere is equal to zero.

  • This implies the absence of magnetic charge, similar to the absence of electric charge deduced from electric field behavior.

Note: If familiar with surface integrals, it can be observed that the magnetic field sums to zero due to the opposite dot product between the surface normal vector and magnetic field direction at the two ends of the imaginary sphere.

• Faraday's Law:

  • A change in magnetic flux induces a voltage.

  • This principle is utilized in transformers for energy transfer and explains the presence of back electromotive force (EMF) voltage in motor coils.

• Ampere's Law:

  • A current-carrying wire induces a magnetic field.

  • This principle is applied in the creation of electromagnets.

In practice

• Faraday's Law governs electromagnetic induction, which is fundamental to the operation of transformers for efficient energy transfer and the generation of back EMF voltage in motor coils.

• Ampere's Law is the basis for creating electromagnets, which find numerous applications across various industries.

By understanding and applying these principles, engineers can design and analyze electromagnetism-based systems and devices, enabling the development of technologies ranging from power distribution to electric motors.