Electromagnetism Fundamentals: Charges, Fields, and Circuits
Coulomb’s Law
The magnitude of each electrical force between two stationary point charges is directly proportional to the product of the magnitudes of both charges and inversely proportional to the square of the distance between them.
Coulomb’s law is valid only in stationary conditions, i.e., when there is no charge movement or when the movement occurs at low speeds and in uniform rectilinear trajectories. This is why it is called electrostatic force.
In mathematical terms, the magnitude 
force that each of the two point charges 
and 
exerts on the other, separated by a distance 
, is expressed as:
Given two point charges
and
separated by a distance
in a vacuum, they attract or repel each other with a force whose magnitude is given by:
Electric Field
The electric field is a physical field represented by a model describing the interaction between bodies and properties of natural systems with electric charge. Mathematically, it is described as a vector field in which a point charge q experiences a force 
given by:
E denotes the electric field.
Lines of Force of an Electric Field
An electric field can be represented by lines of force (no matter), which are useful for studying it.
The lines of force at each point indicate the direction of the electric field (E). These lines never cross each other, and the closer they are, the more intense the electric field. However, for a given electric field, the number of lines of force is constant.
The lines of force of an electric field always start with a positive charge and end on a negative charge.
Electric Potential
The electric potential at a point is the work done by an electrical force to move a positive charge q from a reference point to that point, divided by the unit test charge. In other words, it is the work done by an external force to bring a unit charge q from the reference point to the location being considered against the electric force. Mathematically expressed as: V = W / q
Electric Current
Electric current is a stream of electrons flowing through a material.
Some materials, such as “conductors,” have free electrons that easily pass from one atom to another.
If these free electrons move in the same direction as they jump from one atom to another, they constitute an electrical current.
An external power source is needed to make this movement of electrons in a specific direction.
When a material is placed between two electrically neutral bodies charged with different potentials (they have different charges), electrons move from the body with a more negative potential to the body with a more positive potential. See the figure.
Electrons travel from negative potential to positive potential. However, by convention, the direction of the electric current is considered to go from positive potential to negative potential.
This can be visualized as the space (gap) that the electron leaves to move from a negative to a positive potential. This gap is positive (absence of an electron) and circulates in the opposite direction to the electron.
Electrical current is measured in amperes (A) and is symbolized by the letter I.
So far, we have discussed a current flow that goes from one terminal to another continuously. This current flow is called direct current. There is another case in which the flow of current alternates, first one way and then the opposite. This type of current is called alternating current.
Magnetic Fields
A magnetic field is a region of space in which an electrical point charge moving at a velocity 
experiences a force perpendicular and proportional to both the velocity and the field. This force is described by:
where F is force, v is velocity, and B is the magnetic field, also called magnetic induction or magnetic flux density.
Motion of a Charged Particle in a Magnetic Field
Electric and magnetic fields deflect the trajectories of two moving charges, but do so in different ways. A charged particle moving in an electric field (as produced between the two plates of a capacitor plane arranged horizontally) suffers an electric force F e in the direction of the E field, which bends its path. If the particle reaches the space between the two plates in a direction parallel to the plate deviate + if the charge is negative and to the – otherwise, but always in a vertical plane, ie perpendicular to both plates. This map is defined by the vectors v and E.
If the two plates of the capacitor is replaced by the two poles of a horseshoe magnet, the particle undergoes a magnetic force F m according to the rule of the left hand is perpendicular to the vectors v and B. In this case the trajectory of the charged particle is deflected in the horizontal plane.
Faraday’s Law
The Law of electromagnetic induction Faraday (or just Faraday’s law) states that the induced voltage is directly proportional to the speed with which changes the magnetic flux through a surface with the circuit as a border.
Lenz Law
Lenz’s Law tells us that the induced voltages are in a sense such that opposing magnetic flux variations that occurred. This law is a consequence of the principle of conservation of energy.
The polarity of an induced voltage is such that it tends to produce a current whose magnetic field is always opposed to the existing field variations produced by the original current.
The flow of a uniform magnetic field through a flat circuit is given by:
where:
Φ = magnetic flux . The unit in the SI is the weber (Wb).
B = magnetic induction . The SI unit is the tesla (T).
S = surface of the conductor .
α = angle to form the conductor and the direction of the field .
If the driver is moving, the flow value will be:
In this case, Faraday’s Law states that the ε V induced in each moment is worth:
V ε
The negative value of the above expression indicates that the V ε is opposed to the change in flow that occurs. This sign corresponds to the Lenz law.
Generators
A generator is any device capable of maintaining a potential difference of electricity between two points, calledpoles, terminals or terminals . Electric generators are machines designed to transform mechanical energy into electricity . This transformation is accomplished by the action of a magnetic field on electrical conductors arranged on a frame (also called stator). If mechanically relative movement between the conductors and the field will generate an electromotive force (EMF). Are based on Faraday’s law .
Motors
An engine is part of a machine capable of transforming any type of energy ( electric , of combustible fossils, etc..) in mechanical energy capable of performing a job . In automobiles this effect is a force that produces movement.