Electric Fields of straight wire

[stylez03]

Homework Statement

A very long, straight wire has charge per unit length 1.47×10^10

At what distance from the wire is the electric field magnitude equal to 2.57 N/C

Homework Equations

E = lambda / (2*pi*E_o*r)

E_o = 8.85*10^-9

The Attempt at a Solution

2*pi*E_o*E / lambda = r

Is this correct so far?

 

[Kurdt]

Looks fine you just need to plug the numbers in.

 

[stylez03]

r = 2*pi*(8.85*10^-9)*(2.57) / (1.47*10^-10)

I'm not sure if lambda is represented correctly and is E just 2.57 or should it be 10^(something)

 

[Kurdt]

E will just be 2.57 as stated in the problem. Why are you worried about lambda?

 

[stylez03]

I wasn't sure if lambda = 1.47*10^-10

 

[Kurdt]

probably more likely to be x10^-10 than the other way round.

 

[stylez03]

probably more likely to be x10^-10 than the other way round.

Thats what I had before 1.47 x 10^-10

 

[Kurdt]

What is it in the question?

 

[stylez03]

What is it in the question?

The original question was if lambda = 1.47 x 10^-10.

You said yes, so I just wanted to make sure.

 

[stylez03]

2*pi*(8.85*10^-9)*(2.57) / (1.47*10^-10) = r

This evaluated to:
r = 972

The online program says I'm off by an additive constant??

 

[Kurdt]

I've just noticed you have E on top of the fraction and lambda below. You need to swap these two so the equation is:

$$r=\frac{2k\lambda}{E}$$

Like I said in a previous thread, try manipulating equations with just their symbols until the very last moment. Its a lot easier to spot problems that way.

EDIT: Sorry $$k=\frac{1}{4\pi \epsilon_0}$$

 

[stylez03]

2* (1/4*pi* 8.85*10^-9) * (1.47*10^-10) / 2.57

= 1.03×10−3

Still says I'm off by a additive constant.

 

[Kurdt]

I think you've made a mistake in the calculation as i get a different answer. Try it again you're 3 orders of magnitude out.

 

[Kurdt]

Where did you get that value of epsilon nought from? It should be: 8.85x10^-12

 

[stylez03]

Where did you get that value of epsilon nought from? It should be: 8.85x10^-12

I need to be more careful from paper to online input. I have so much scratch work, some how I changed the epsilon value =[

 

[Kurdt]

No problem. Try a bit of latex for your equations it should help in future to diagnose problems quicker

https://www.physicsforums.com/showthread.php?t=8997