physics

Magnetic fields and moving charges

Each of these fields can be modeled as a point charge q, that moves at the velocity v in a specific direction; where the magnetic field B, at distance r and angle q to direction of movement, is given as:  

Lorentz Force

The Lorentz force describes the interaction between a moving charge and the magnetic field, with the force F acting perpendicular to both the magnetic field B and the velocity (v) of the charged particle (q). It is mathematically expressed as:

F = q v B sin α

where α is the angle between the direction of motion and the magnetic field 

In a current of charges flowing through a conductor, the Lorentz force acts on both the individual particles and on the conductor as a whole. Therefore, the individual forces add up to:

F = I d B sin α

Where d is the length of the electrical conductor. 

Magnetic flux

The magnetic flux (ΦB) through a surface is defined as the product of the magnetic field (B), the area (A) it penetrates, and the cosine of the angle (θ) between the field and the surface:

ΦB = n B A cosθ

where n represents the number of turns in a coil. The unit of magnetic flux is the weber, where 1 Wb = 1 T m^2

Unlike the electric currents, the magnetic flux lines are not bound by the geometry of the conductor. Magnetic field lines form closed loops and are perpendicular to the direction of changes in the magnetic field. When the flux changes and isnt constant through the coil, an induced voltage arises in eaach turn of the coil.

This behaviour is captured by Faraday's Law of Induction, which states that a changing magnetic field induces an electromotive force (EMF) or voltage in a conductor. This induced EMF generates a current, producing an electric vortex field.

There is no positive or negative potential that could serve as sources of the electrical field. Instead we have closed field lines that are created perpendicular to the direction in which the magnetic field changes. 

Generation of Electric fields

The process doesn’t end here. A changing magnetic field induces a voltage, which generates an electric current in the conductor through an electric vortex field. This induced current, in turn, produces its own magnetic field. 

According to Lenz's Law, the induced voltage opposes the original change in the magnetic field, resisting the change. The system essentially resists the change by creating a force that counters it, and overcoming this resistance requires the input of energy.

The process is self-sustaining, with the induced electric and magnetic fields interacting dynamically. Such principles are foundational in technologies like generators, transformers, and MRI machines.