Electromagnetic TheoryPublished on 24/2/2012 & updated on 26/7/2018
Before learning Maxwell’s Equations, we need to learn 3 Mathematical operations which are basic entities of the equations. The Del operator refers to the partial differentiation of a function. We represent it as ∇ (Nabla). Grad f gives the gradient of a function i.e. grad f = ∇f, which means the partial differentiation of a function with respect to x, y and z-axis in a 3 - dimensional domain. The gradient is a vector quantity. The Divergence operator of a vector quantity gives us a scalar entity, which represents the rate at which the density exits a given range of space. It is represented as div v = ∇.v. The Curl represents the rotation of a vector in a three-dimensional field. It is denoted by Curl v = ∇ x v. The 4 basic Maxwell’s Equations are as follows:- Here, ρ represents net charge inside the surface, ε0 represents permittivity of vacuum, B represents the magnetic field, E represents electric field and J represents current density. The first law states that the electric flux which forms across a closed surface is proportional to the charge enclosed. The second law states that the magnetic flux induced across a closed surface is zero. The third law states that the magnetic fields which vary with time lead to an electric field. The fourth law states that that time-varying Electric fields or steady currents lead to a magnetic field.
Hence, as shown by the above equations, it is proved that a varying electric field leads to a magnetic field and a varying Magnetic field leads to an electric field. The solution of Maxwell’s equations is a three-dimensional equation which represents a wave travelling at the speed of light. The electromagnetic energy waves carry energy through empty space and this energy is used for a variety of applications such as Remote sensing techniques, Radio waves, Ultraviolet (UV) rays and many more.
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