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On the other hand, if a sphere of radius R is charged so that the top half of the sphere has uniform charge density and the bottom half has a uniform charge density then the sphere does not have spherical symmetry because the charge density depends on the direction ( (Figure)(b)).

For instance, if a sphere of radius R is uniformly charged with charge density then the distribution has spherical symmetry ( (Figure)(a)). In other words, if you rotate the system, it doesn’t look different. To exploit the symmetry, we perform the calculations in appropriate coordinate systems and use the right kind of Gaussian surface for that symmetry, applying the remaining four steps.Ĭharge Distribution with Spherical SymmetryĪ charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. A charge distribution with planar symmetry.A charge distribution with cylindrical symmetry.A charge distribution with spherical symmetry.The field may now be found using the results of steps 3 and 4.īasically, there are only three types of symmetry that allow Gauss’s law to be used to deduce the electric field. Evaluate the electric field of the charge distribution.

It is often necessary to perform an integration to obtain the net enclosed charge. This is an evaluation of the right-hand side of the equation representing Gauss’s law. Determine the amount of charge enclosed by the Gaussian surface.The symmetry of the Gaussian surface allows us to factor outside the integral. Evaluate the integral over the Gaussian surface, that is, calculate the flux through the surface.

With this choice, is easily determined over the Gaussian surface. Choose a Gaussian surface with the same symmetry as the charge distribution and identify its consequences.As examples, an isolated point charge has spherical symmetry, and an infinite line of charge has cylindrical symmetry. This is an important first step that allows us to choose the appropriate Gaussian surface. Identify the spatial symmetry of the charge distribution.