What is the E Field Due to a Line of Charge in 3D?

[Drpepperment]

Homework Statement

What is the E Field due to a Line of Charge?

All physics classes, books and sites I've visited on the internet set this problem up in the exact same way -- the line of charge is restricted to an axis (usually the x-axis) and the point is floating over it. For my simulation, the finite line of charge might be anywhere, and the point might be anywhere in 3D. To overcome this, my previous solution was to rotate my frame of reference into http://www.gamedev.net/topic/598246-quaternion-rotation/" so that I could solve the integral using the standard textbook method. This seemed to work, but I felt that I could save a lot of cycles by figuring out how to do the integration directly.

I have attempted to do this for a 2D example. Here, I parameterize my line as a function of time, letting time range from 0 to 1. Then I integrate with respect to t. On paper, everything looks like it should work. But when I plug in values, the results don't add up. Please see this picture for an example. The first solution is using the textbook method and setup for solving. I get Ex=-0.2163 and Ey=0.3121. When I use my method, the answers come out as Ex=-0.0270 and Ey=0.03901.

What am I doing wrong?? I should be able to do the 't' thingy because we do the exact same thing with theta for curves... I based my work off of http://www.kwantlen.bc.ca/science/physics/faculty/mcoombes/P1220_Notes/EFields/ElectricFieldandPotentialbyDirectIntegration.htm" .

Homework Equations

Located On Image

The Attempt at a Solution

[PLAIN]http://authman.net/question.jpg

My https://www.physicsforums.com/showthread.php?t=484718" can be found here. This time, I've completely worked out the new Integral. It's ust the solution that isn't coming out the same.

 

[mark726]

Hi there,

It seems like you are on the right track with your approach to solving this problem. However, there may be a few things that you are overlooking.

Firstly, when integrating with respect to time, you need to make sure that you are using the correct limits of integration. In your example, you have set t = 0 to t = 1, but this may not be the appropriate range for your problem. You should check your parameterization of the line of charge and make sure that the limits of integration are appropriate for the given problem.

Secondly, it is important to consider the direction of the electric field at each point. In your solution, you have only calculated the magnitude of the electric field, but not its direction. You need to make sure that you are taking into account the direction of the electric field when performing the integration.

Lastly, it may be helpful to check your calculations and make sure that you are using the correct equations and values for your problem. It is always a good idea to double check your work to avoid any mistakes.

I hope this helps and good luck with your simulation!