Charge distribution on an irregular conducting surface

[Aman Chauhan]

I recently read that the charge density is less on surfaces with greater radius of curvature on the surface of a charged irregular conducting body . if anyone can provide a proof or explanation , please help!

 

[mfb]

That is not always true, but often it is a good approximation.
Consider two spheres of different size far away from each other at the same potential. If you calculate their electric field strengths at the surface, you will see that the smaller sphere has the stronger field, which corresponds to a larger charge density.

 

[officialmanojsh]

That is not always true, but often it is a good approximation.
Consider two spheres of different size far away from each other at the same potential. If you calculate their electric field strengths at then surface, you will see that the smaller sphere has the stronger field, which corresponds to a larger charge density.

Agreed! Because when there is same potential on both smaller and larger spheres, the charged atoms on smaller sphere will be very near where as due to more area of larger sphere, there is not space between charges atoms. Here both the potential difference and radius of curvature in case of spheres matters. :)

 

[Aman Chauhan]

I am able to understand your explanation . But how can you say that this situation of 2 different sized spheres is equivalent to an irregular body which is just more curved at some points.

 

[mfb]

Every part of the surface is at the same potential. If the more curved parts are exposed, the situation is similar to the small sphere. If they are hidden somewhere in a notch, their charge density can be small.

 

[Aman Chauhan]

Sorry I could not understand what you meant by "hidden somewhere in a notch". please elaborate a bit.

 

[mfb]

Like this:

 

[Aman Chauhan]

Is this low charge density at the notch due to great repulsion from nearby charges (i suppose) Or is there some other reason ?

 

[mfb]

It is low due to the specific geometry here.

The electric potential is roughly the same everywhere in the notch (it is exactly the same everywhere at the surface!), which leads to low charge concentrations at the surface.

 

[Aman Chauhan]

OK, So since the potential at every surface has to be the same and there is more surface nearer to a point in the notch so the charge density has to be less there in order to make the potential same as that of every point. Is that what you meant? (a rough approx. I mean)

 

[mfb]

The surface area has nothing to do with that, and there is no meaningful relation between potential (as absolute value) and charge density here.
The electric field is weaker, and surface charge density is proportional to the field at the surface.