For instance, if a sphere of radius R is uniformly charged with charge density ρ 0 ρ 0 then the distribution has spherical symmetry ( Figure 6.21(a)). In other words, if you rotate the system, it doesn’t look different. Charge 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. 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. 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 E → n ^ d A over the Gaussian surface, that is, calculate the flux through the surface. ![]()
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