Gauss' law: find the electric field

[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

 

[kuruman]

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?

 

[Alice7979]

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]

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.

 

[vela]

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.

 

[Alice7979]

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