Gaussian surfaces are chosen based on the known symmetry of the charge distribution. For any spherically symmetric charge distribution, you know that the electric field must be radial with constant magnitude at any specific distance from the center of symmetry, so you use a spherical surface for the Gaussian integral. For a uniform plane of charge, or just outside the surface of a metal, you know the field must point directly away from the surface and be constant at any given distance from it. The Gaussian "pillbox" exploits this symmetry to make the integral trivial to evaluate. Inside a metal, the field must be zero, so a closed surface everywhere within a metal yields a zero Gaussian integral. When there is no symmetry, Gauss' Law is still valid, but not particularly useful.misogynisticfeminist said:I wonder if i could compute resultant E-fields using Gauss' law and finding the field from the flux. I have a few difficulties, the first is of course, finding the E-field from the flux and the second is regarding the closed surface. how should i choose what surface to use, especially if the question just want me to find the resultant E-field alone? Thanks...
Gauss' Law is a law in physics that relates the distribution of electric charges to the resulting electric field. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.
Gauss' Law can be used to solve for electric fields by choosing an appropriate Gaussian surface, calculating the electric flux through that surface, and equating it to the enclosed charge divided by the permittivity of free space. This allows us to find the magnitude and direction of the electric field at any point in space.
Some common surfaces used when solving for electric fields using Gauss' Law include spherical surfaces, cylindrical surfaces, and planar surfaces. The choice of surface depends on the symmetry of the charge distribution and the simplicity of the resulting calculations.
Choosing a closed surface is necessary when using Gauss' Law because it allows us to enclose the entire charge distribution and accurately calculate the electric flux through the surface. This ensures that the resulting electric field is complete and takes into account all of the charges present.
If the chosen surface does not enclose the entire charge distribution, the resulting electric field calculated using Gauss' Law will only be a portion of the true electric field. This can lead to inaccurate results and must be taken into consideration when choosing a surface for solving electric fields.