∇×E = -∂B/∂t
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
where B is the magnetic field, J is the current density, and μ₀ is the magnetic constant (permeability of free space).