Solving E-Fields using Gauss' Law: Choosing Surfaces

[misogynisticfeminist]

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...

 

[OlderDan]

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...

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.

 

[thepatientmental]

Yes, you can use Gauss' Law to compute resultant E-fields by finding the field from the flux. This method is often used in situations where the geometry of the electric field is difficult to determine.

Regarding your difficulties, finding the E-field from the flux can be done by using the relation E = Q/ε0A, where Q is the enclosed charge, ε0 is the permittivity of free space, and A is the surface area. This equation can be used for any closed surface, as long as the enclosed charge and surface area are known.

As for choosing the closed surface, it is important to consider the symmetry of the electric field. Gauss' Law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. Therefore, choosing a closed surface with high symmetry can simplify the calculation and make it easier to find the enclosed charge.

If the question only asks for the resultant E-field, then you can choose any closed surface that is convenient for you to calculate. However, if the question asks for other information such as the electric field at a specific point, then you may need to choose a closed surface that passes through that point.

I hope this helps with your understanding of solving E-fields using Gauss' Law. Keep practicing and you will become more comfortable with choosing appropriate surfaces and solving for resultant E-fields. Good luck!