# HOW to think about surface charge and voltage?

1. Oct 1, 2012

### bingbong

HOW to think about surface charge and voltage!?

1. The problem statement, all variables and given/known data
I'm just trying to think about something that's confusing the hell outta me. If a charge q+ is near a grounded conducting sphere, where the voltage at the surface is zero, we can use image charges to find the electric field and potential at all points OUTSIDE of the sphere, right? q+ is going to induce a surface charge on the sphere, which means that there are going to be electrical field lines on the surface...but how can there be no voltage on the surface, if the charge is distributed so as to cancel the field lines from q+??

2. Relevant equations

3. The attempt at a solution
I figured out the potential by creating an image charge q' in the sphere and summing up the voltage at some point R outside of the sphere from q and q'. I just don't know how to think about voltage being zero at the surface and the existence of a surface charge

Last edited: Oct 1, 2012
2. Oct 2, 2012

### ehild

Re: HOW to think about surface charge and voltage!?

The conducting sphere is grounded, connected to the Earth, so the potential is zero on (it if you take the potential of the ground zero). The Earth can be the source of any charge, therefore the external positive charge q+ attracts negative charges from the ground, which accumulate on the surface of the conducting sphere. That surface charge distribution can be replaced by the image charge so as the electric field of the external charge and image charge is the same as that of the external charge and the surface charge density. The surface charges do not cancel the electric field lines emerging from q+: the field lines emerging from q+ end in the surface charges or in the image charge.

Think of a parallel plate capacitor: One plate is grounded (its potential is zero), the is other charged to Q+, it is at a positive potential. There is Q- charge on the grounded plate, electric field lines between the plates and the potential of the grounded plate is zero.

ehild