Electrostatics and Magnetism: Key Principles and Laws
Electrostatics and Magnetism: Key Principles
Coulomb’s Law
The force of attraction or repulsion between two point electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. The force is directed along the straight line joining the charges. It is repulsive if the charges have the same sign and attractive if they have opposite signs. These are distance forces, and no material medium is needed between the charges. It also adheres to the principle of action and reaction and the principle of superposition.
Electric Field
An electric field is a disturbance produced by a charged body in the surrounding space. It is a radial, central field, and its direction depends on the sign of the charge (q).
Electric Potential Energy
The electric potential energy of a charge (q) at a point in space is the work done by the electric field to move the charge (q) from that point to infinity.
Electric Potential
The electric potential at a point in space is the work done by the electric field to move a unit positive charge from that point to infinity.
Field Work
Positive Field Work (Spontaneous)
The charge (q) is moved by the action of the electric field forces. The charge (q) decreases its electric potential energy. This occurs when two charges of the same sign are separated or when two charges of opposite signs come closer.
Negative Field Work (Non-Spontaneous)
The charge (q) moves through the action of an external force. The charge (q) increases its electric potential energy. This occurs when two charges of the same sign come closer or when two charges of opposite signs are separated.
Electric Flux
The electric flux through a surface is a measure of the number of field lines that cross the surface. The electric flux through a closed surface (S) is proportional to the net electric charge (Q) enclosed by the surface, divided by the dielectric constant.
Magnetism
Magnetic Field
A magnetic field is a perturbation produced by a magnet or an electric current in the space around them.
Biot-Savart Law
The Biot-Savart law describes the magnetic field created by a moving charge (q) or steady currents. For circuit currents in a filiform (or closed) loop, the contribution of an infinitesimal element of length (dl) of the current path (I) creates a basic contribution of magnetic field (dB) at a point, with the position vector (Ur) at a distance (R) with respect to (dl), pointing towards the current (I).
Lines of Magnetic Induction
The magnetic field created by a current has lines of magnetic induction that are circumferences. The center of these circumferences is at the conductor, and the direction is given by the right-hand rule.
Ampere’s Theorem
The circulation of the magnetic field on any closed curve (C) is the product of the permeability by the intensity of the electric current passing through the area bounded by the closed curve (C).
Magnetic Flux
Magnetic flux is a measure of the number of lines of magnetic induction that cross a surface.
Faraday-Henry Law
When the number of lines of magnetic induction through the surface of an electrical circuit varies, an electric current is induced.
Lenz’s Law
The direction of the induced current is such that it opposes the cause that produces it.
Faraday’s Law
The induced electromotive force is related to the variation of the magnetic flux.
Maxwell’s Equations
Maxwell summarized all the laws of electricity and magnetism into four fundamental equations.
Gauss’s Law
For the Electric Field
The electric flux passing through any closed surface is proportional to the electric charge enclosed.
For the Magnetic Field
The magnetic flux through any closed surface is zero.
Faraday’s Law of Electromagnetic Induction
A variable magnetic field generates an electric field around it.
Ampere-Maxwell Law
A magnetic field can be produced by an electric current or a variable electric field.