Image charges of a 30 degree corner

[physapple89]

Homework Statement

I just want to make sure I'm doing this right. okay so you have a conducting corner of angle 30 degrees. How many image charges are there, I just need to sketch it.

Homework Equations

The Attempt at a Solution

my book sucks only explaining it for a 90 degree angle but I'm betting that in order to cancel the voltage for a 30 degree angle you need more than the three in my book. my graph is 11 image charges (because the 360 degrees is broken up evenly so they will cancel out and the angles this works for are 180/n because the 360/n need an even integer for there to be no charges of the same sign right next to each other. ) so I'm getting 11 image charges radially spaced starting wtih the first charge and the next two being perpendicular with teh same distance through the corners to make them V=0 and repeating around the graph.

 

[mark726]

Hello! It sounds like you are on the right track. For a conducting corner of angle 30 degrees, you will need a total of 11 image charges to cancel out the voltage. This is because the 360 degrees is broken up evenly into 12 parts, so there will be 11 image charges radially spaced. The first charge will be at the corner, and then the next two will be perpendicular to each other and equidistant from the corner. This pattern will repeat around the graph, resulting in a total of 11 image charges. Good job on your solution!