Gauss's law states that the total electric flux through a closed surface is proportional to the charge enclosed within that surface. Mathematically, it is expressed as:
Faraday's law states that a changing magnetic field induces an electric field. Mathematically, it is expressed as:
where E is the electric field, ρ is the charge density, and ε₀ is the electric constant (permittivity of free space).
The study of electromagnetics begins with vector analysis, which is a mathematical framework for describing physical quantities with both magnitude and direction. Vectors are used to represent electric and magnetic fields, and various operations such as addition, subtraction, dot product, and cross product are used to manipulate and analyze these fields.
∇×B = μ₀J
The magnetic field is a vector field that represents the force per unit current on a test current. It is produced by current-carrying conductors and is described by the Biot-Savart law. The magnetic field is a solenoidal field, meaning that it can be expressed as the curl of a vector potential.