Fields - ABridgeTooFar/ThreeAmpsAtFiveVolts GitHub Wiki
This site presents a cursory refresher of some of the fundamentals of field theory as it pertains to electric circuits and power-supplies. A similar treatment of the material can be found in further detail at Khan Academy
Fundamental particles of matter are defined by three properties:
-
gravitational mass, represented by
-
electrical charge, represented by
-
magnetic potential, represented by a vector A and a scalar
, and related to the particle's relative velocity
For each of the above properties, there exists an equation that defines the strength of physical force exerted on the particle due to other particles of matter in the vicinity. This force is experienced equally in strength but opposite in direction by the neighbouring particle. We use the primed version of mass , charge
, and velocity
to refer to the neighbour's properties.
The force due to the electrical charge is calculated using Coulomb's Law as:
where is the permittivity of free space and r is the radius separating the particles.
Given a particle with known properties, fields can be used to describe the force experienced by any neighbour that comes near. This is useful since it separates the known properties from the unknowns. The unknown is the electric charge of the neighbour. All other values are known and determined by the first particle.
We can precompute the known quantities for all distances from the first particle. The chart of the resulting magnitudes and directions is called the electric field of the particle. The force felt by any particle in the area of the chart is the product of the field and the arbitrary charge the neighbour.
In spherical coordinates, the electric field of a particle located at the origin of a chart is computed as: