# Gauss' law: find the electric field

## 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

kuruman
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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?

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?

kuruman
Homework Helper
Gold Member
2021 Award
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
vela
Staff Emeritus