# Problem with electrostatics

## Homework Statement

I'm suppose to set a general function of the electric field, at any point in the xy plane. As the picture shows, there are 2 point charges with 1 charge, and 1 point charge with -3 charge. Each of them are equally distanced from the origin, and all 3 are evenly spaced apart.

## Homework Equations

I'm used Coulumbs law

## The Attempt at a Solution

First I defined all the point charge locations, along with an arbitrary point, to represent the unknown point of the function.

Then I merely use Coumlumbs law, to add up all the expressions:

The final expression isn't pretty at all though:

The field as displayed by maple (if one fixes the fieldstrength, otherwise some arrows become very very small) looks like this:

Which to me looks about right. However the vector function isn't divergence free, which suggests I have messed up something. What am I doing wrong?

#### Attachments

4.9 KB · Views: 528
1.2 KB · Views: 184
2.7 KB · Views: 216
579 bytes · Views: 191
2.7 KB · Views: 184
607 bytes · Views: 182
5.9 KB · Views: 215
28.4 KB · Views: 203

Homework Helper
Gold Member
The two dimensional function will not be divergence free, but if you included the z-component of the electric field, it would then be divergence free except at the locations of the electrical charges. ## \\ ## I didn't carefully check your equations, but they seem to be correct.

NicolaiTheDane
The two dimensional function will not be divergence free, but if you included the z-component of the electric field, it would then be divergence free except at the locations of the electrical charges. ## \\ ## I didn't carefully check your equations, but they seem to be correct.

Ahh alright then. Thanks a bunch! :)