Here, E= The magnitude of the given electric fieldĭS= Surface area Electric Flux and the Gauss’s Law Electric Flux for a Non-Uniform Electric Fieldįor a given non-uniform field, the formula for the electric flux through a small surface area is as follows: Θ = The angle formed between the electric field lines and the normal to S. If the given electric field is uniform, then the electric flux passing through the surface will be:Į= The magnitude of the given electric field Electric Flux for a Uniform Electric Field The electric flux will be the rate of flow of the electric field of any given area and is also proportional to the electric field lines. The electric flux, being a scalar quantity, only has magnitude but no direction, and the unit of electric flux is Nm 2 /C ( Newton-meters squares per coulomb ). The famous Gauss’s law shows the mathematical relation between electric flux and enclosed charge. As the magnitude of positive electric flux is equal to the negative electric flux, the net electric flux will be zero. If every field line directed into the surface continues from the interior and directs towards the outward someplace else than the surface, there will be no net charge within the closed surface. Similarly, if the field lines are directed away from the closed surface, it will be positive. Moreover, the electric field lines directed on a closed surface will be negative. These field lines originate on the positive charge and end on the negative charge. It can also be thought of as the number of electric field lines intersecting at a given area. If the charge distribution lacks sufficient symmetry for the application of Gauss' law, then the field must be found by summing the point charge fields of individual charge elements.Electric flux is the measure of an electric field or it is the method of describing the electric field strength at a specific distance from the causative charge of the field. Gauss' law is a powerful tool for the calculation of electric fields when they originate from charge distributions of sufficient symmetry to apply it. When the area A is used in a vector operation like this, it is understood that the magnitude of the vector is equal to the area and the direction of the vector is perpendicular to the area. If the area is not planar, then the evaluation of the flux generally requires an area integral since the angle will be continually changing. The electric flux through a planar area is defined as the electric field times the component of the area perpendicular to the field. The concept of electric flux is useful in association with Gauss' law. Gauss' law permits the evaluationof the electric field in many practicalsituations by forming a symmetric Gaussian surface surrounding a charge distribution and evaluating the electric flux through that surface. Gauss' law is a form of one of Maxwell'sequations, the four fundamental equationsfor electricity and magnetism. Gauss' Law, Integral Form The area integral of the electric field over any closed surface is equal to the net charge enclosed in the surface divided by the permittivity of space. HyperPhysics***** Electricity and Magnetism If it picks any closed surface and steps over that surface, measuring the perpendicular field times its area, it will obtain a measure of the net electric charge within the surface, no matter how that internal charge is configured. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.Īnother way of visualizing this is to consider a probe of area A which can measure the electric field perpendicular to that area. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. Gauss's Law is a general law applying to any closed surface. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. Gauss's Law Gauss's Law The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.
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