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There are four basic equations in electromagnetism which govern the electrodynamics. These equations are derived from some of the fundamental laws in electricity as well as in magnetism. They can be treated in both in free space as well as in a dielectric. The Maxwell’s equations in free space in the absence of any dielectric or magnetic material are as follows:
(i) Gauss’s law in electricity: This law states that the total electric flux through any closed surface equals the net charge inside that surface divided by the permittivity in free space and is given as follows:
(ii) Gauss’s law in magnetism: It states that the net magnetic flux through a closed surface is zero and is given as:
That is, the number of magnetic field lines that enter a closed volume must equal the number that leaves that volume. This implies that the magnetic field lines cannot begin or end at any point. If they do so, then it would imply the existence of isolated magnetic monopoles. However, it is not possible in nature.
(iii) The third equation is obtained from Faraday’s law of induction. It implies that changing the magnetic field can create an electric field. This law states that the emf, which is the line integral of the electric field around any closed path, equals the rate of change of magnetic flux through any surface area bounded by that path. The consequent equation is given as follows:
This implies that the time varying magnetic field is responsible for induction of current in a conducting loop.
(iv) The fourth equation is derived from Ampere-Maxwell law and implies that magnetic field can be created by an electric field and electric current. It is given as follows:
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