# Gauss' law: find the electric field

• Alice7979
In summary, the homework statement says that a wire with a positive charge of 4.1 × 10-8 C is distributed uniformly along it. The electric field at a radial distance of 3.2 cm has a magnitude of 8.85E-12.
Alice7979

## Homework Statement

A long, thin, straight wire of length 1.3 m has a positive charge 4.1 × 10-8 C distributed uniformly along it. The electric field created by this wire at a radial distance 3.2 cm has a magnitude of
ε= 8.85E-12

## Homework Equations

I think I need to use E= q/(4πr^2ε) but I don't know what to do with 1.3 m.

## The Attempt at a Solution

E= 4.1E-8/(4π(.032^2)(8.85e-12) =360023.43

You need to use Gauss's Law as the problem suggests. The equation that you have as "relevant" is applicable to a point charge, not a line of charge. Is the electric field given or are you looking for it?

kuruman said:
You need to use Gauss's Law as the problem suggests. The equation that you have as "relevant" is applicable to a point charge, not a line of charge. Is the electric field given or are you looking for it?
E= Q/εA
I can't find another equation in my notes but from the internet I found this one. Is it right?

It is right for a certain class of problems that involve infinite sheets of charge. This is not what you have here so it's not right for this problem. You have to understand that different charge distributions generate different kinds of fields which require different mathematical expressions. Now all these expressions use E as the symbol for the electric field. So when you grab an expression from the internet, you have to pay attention to what kind of charge distribution that expression corresponds to and make sure it matches the problem that you have.

The problem is asking you to use Gauss's Law because this exercise is designed to teach you how to apply it to problems with cylindrical symmetry. Now you can follow that suggestion or you can find a formula from the internet if you use the right search parameters to narrow the search down to the electric field that you have. So the question is do you want to learn how to use Gauss's Law or do you want to learn how to do better internet searches on electric fields? The choice is yours, but you need to consider that during a test one is usually not allowed to do internet searches.

Last edited:
Delta2
Alice7979 said:
I can't find another equation in my notes but from the internet I found this one. Is it right?
Do you have a textbook? I'm sure it has examples which are relevant to this problem.

With electromagnetism, it's really not a good idea to use the "find the formula and plug the numbers in" approach. You want to spend time understanding where the various formulas come from, otherwise you're likely going to feel overwhelmed by the plethora of similar formulas.

the area was wrong, it just had to be 2x3.14rl

## 1. What is Gauss' law?

Gauss' law is a fundamental law of electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface.

## 2. How do you use Gauss' law to find the electric field?

To use Gauss' law to find the electric field, you first need to choose a closed surface that encloses the charge distribution. Then, calculate the electric flux through that surface and equate it to the charge enclosed divided by the permittivity of free space.

## 3. What is the equation for Gauss' law?

The equation for Gauss' law is ∮E⃗ · dA⃗ = Qenc/ε0, where E⃗ is the electric field, dA⃗ is a small area element on the closed surface, Qenc is the total enclosed charge, and ε0 is the permittivity of free space.

## 4. Can Gauss' law be applied to any charge distribution?

Yes, Gauss' law can be applied to any charge distribution as long as the closed surface chosen encloses the entire charge distribution.

## 5. How is Gauss' law used in practical applications?

Gauss' law is used in practical applications such as calculating the electric field around a point charge or a spherical charge distribution, determining the electric field inside a charged conducting sphere, and analyzing the electric field in various geometries such as cylinders, planes, and spheres.

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