If N field lines pass through S 1 S 1, then we know from the definition of electric field lines ( Electric Charges and Fields) that N / A 1 ∝ E, N / A 1 ∝ E, or N ∝ E A 1. To quantify this idea, Figure 6.4(a) shows a planar surface S 1 S 1 of area A 1 A 1 that is perpendicular to the uniform electric field E → = E y ^. Again, flux is a general concept we can also use it to describe the amount of sunlight hitting a solar panel or the amount of energy a telescope receives from a distant star, for example. Similarly, the amount of flow through the hoop depends on the strength of the current and the size of the hoop. As you change the angle of the hoop relative to the direction of the current, more or less of the flow will go through the hoop. The numerical value of the electric flux depends on the magnitudes of the electric field and the area, as well as the relative orientation of the area with respect to the direction of the electric field.Ī macroscopic analogy that might help you imagine this is to put a hula hoop in a flowing river. 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.Figure 6.3 The flux of an electric field through the shaded area captures information about the “number” of electric field lines passing through the area.
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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