How do you determine the limits of integration for a Gauss' Law problem?

Question

I have trouble understanding Gauss' law problems mostly because I can never determine the limits of integration for them. Some examples would be much appreciated so I can learn from examples.

Lily Adams · Accepted Answer

Integrate the field without any integration limits to obtain the potential.

That is your potential. An extra constant doesn't make a difference to the field. And the field is the quantity you wish to work with. Potential is simply a tool to facilitate evaluation of fields.

When obtaining potential from integrating the expression for field, you can set zero potential at some reference point depending on the problem. Once you've done that, you can evaluate the constant and hence the required expression for potential.

Amelia Adams · Answer

undefined To determine the limits of integration for a Gauss' Law problem, you typically need to identify the region of space where the electric field is being calculated. This involves considering the geometry and symmetry of the charge distribution. Once you have identified the relevant surface enclosing the charge distribution, you select a suitable Gaussian surface and determine the limits of integration based on the coordinates or parameters describing the surface. These limits ensure that the integral covers the entire surface area of the Gaussian surface.