# Determining electric field using gauss's law--different distributions

• Helenah
In summary, the conversation discusses the use of Gauss's law to determine the electric field of four different distributions. The speaker is trying to determine which distributions can effectively use Gauss's law, and mentions that all four distributions have charges. They also mention the possibility of using Q/(A*electric constant) to calculate the electric field, but are unsure if they can use Gauss's law for all four distributions. The conversation also explores the concept of symmetry and how it relates to the use of Gauss's law. The speaker points out that distributions A and D may not be symmetric enough to use Gauss's law, while distributions B and C may be more suitable. The conversation ends with a prompt to explain how Gauss's law can be used in cases B
Helenah
Homework Statement
We are supposed to determine which (if any) of the distributions will need to/could use Gauss's law to determine the electric field
Relevant Equations
flux = Q/electric constant = EA

These are the 4 distributions shown, and I have to determine which two distributions (or none at all) can use Gauss's law to determine the electric field.

So electric flux = EA = Q/electric constant.

Since all of them have charges, I could do something like Q/(A*electric constant) to get the electric field—that's where I'm confused, because I think I could actually use Gauss's law on all four of them. The only other way I can think of is that Gauss's law is applied to surfaces so that probably excludes lines (A) and disks (D), which do not really have surface area.
Am I right in thinking so? Is there a better / correct way to get to the answer?

Last edited:
You perhaps need to think about how you would practically use Gauss's law to determine the electric field.

@PeroK
Hmm. Distribution A could potentially be viewed as line of charge + imaginary cylinder to get some electric field, but the charges aren't symmetric and hence will not be able to use gauss's law (?).
I'm not sure where else it's not symmetric though.

Helenah said:
@PeroK
Hmm. Distribution A could potentially be viewed as line of charge + imaginary cylinder to get some electric field, but the charges aren't symmetric and hence will not be able to use gauss's law (?).
I'm not sure where else it's not symmetric though.
The trick to use Gauss's law effectively is to have a surface across which the electric flux must be constant.

Your intuition is right that A and D are problematic and B and C are better. Can you explain more clearly how you do things in cases B and C?

## 1. How do you determine the electric field using Gauss's Law?

The electric field can be determined using Gauss's Law by calculating the electric flux through a closed surface surrounding the charge distribution. This can be represented mathematically as E = Φ/ε0, where E is the electric field, Φ is the electric flux, and ε0 is the permittivity of free space.

## 2. What are the different types of charge distributions that can be analyzed using Gauss's Law?

There are three main types of charge distributions that can be analyzed using Gauss's Law: point charges, line charges, and surface charges. Point charges have a single point of concentration, line charges have a linear distribution of charge, and surface charges have a two-dimensional distribution of charge.

## 3. Can Gauss's Law be used for non-uniform charge distributions?

Yes, Gauss's Law can be used for non-uniform charge distributions. In these cases, the electric field is determined by dividing the charge distribution into smaller, more manageable parts and calculating the electric field for each part. The total electric field is then found by summing up the individual electric fields.

## 4. What is the significance of choosing a Gaussian surface when using Gauss's Law?

The choice of a Gaussian surface is important when using Gauss's Law because it determines the symmetry of the charge distribution. The electric field can only be determined using Gauss's Law if the charge distribution has a certain degree of symmetry, such as spherical, cylindrical, or planar symmetry. The Gaussian surface must also be chosen so that it encloses the entire charge distribution.

## 5. How does the electric field vary with distance from a point charge when using Gauss's Law?

When using Gauss's Law to determine the electric field from a point charge, the electric field varies inversely with the square of the distance from the charge. This means that as the distance from the charge increases, the electric field decreases. This relationship is represented mathematically as E ∝ 1/r2, where E is the electric field and r is the distance from the charge.

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