# Gauss's Law

Gauss's law is a mathematical law that relates electric flux, magnetic flux, and electric and magnetic fields in a magnetic vector field, such as a magnetic field or magnetic field of a current-carrying wire. The law, which is named after German mathematician Carl Friedrich Gauss, is the starting point of vector calculus, which is a branch of mathematics dealing with the concepts of magnitude and direction in a vector field. The law states that the total magnetic flux through a surface is proportional to the magnetic field at that surface. The law derives from Faraday's law of induction, which states that the induced voltage is proportional to the rate of change of magnetic flux through a surface. The induced current is proportional to the length of the surface perpendicular to the magnetic flux. In the magnetic induction formula the magnetic flux is the electric field divided by the area, so the total magnetic flux is the flux through the surface times the area, and the total magnetic field is the magnetic induction times the area. The law is used in the construction of electric circuits or magnetic circuits where it is useful to relate the magnetic field and electric field, such as the case of an electromagnet. In the case of an electromagnet, the magnetic field is proportional to the current density and the magnetic flux is proportional to the electric charge, so the law can be used to relate the two quantities. Gauss's law is used in the design of devices, such as electric motors and generators, which use electromagnetism. The law is used in the design of electric and magnetic circuits, in the analysis of the behavior of magnetic materials, such as ferromagnets and antiferromagnets, and in the analysis of the performance of electric circuits and electric motors. The law is used in wire modelling to model non-ideal magnetization of magnetic materials. The law is used in the design of magnetic data storage devices that use magnetic fields to represent data. Electric field Magnetic field Electric flux Magnetic flux