Charge at the center of a conducting sphere

[Idoubt]

If you place a charge +q at the exact center of a conducting sphere, will it stay there or move to the surface?

 

[Bill_K]

It will be in unstable equilibrium. Move it the slightest bit off center and it will continue to move in that direction.

 

[Idoubt]

that's what I thought too thx

 

[Discord7]

If you place a charge +q at the exact center of a conducting sphere, will it stay there or move to the surface?

If the surface of the sphere were to possesses a greater but opposite charge, I think any internal charge would remain or move into the center.

 

[Idoubt]

thinking it over, i think the surface of the sphere might develop a net negative charge -q so that the electric field inside is zero.

the +q charge at the center will shift electrons towards it thus positive charge is shifted radially outward until it reaches the surface of the sphere.

any thoughts?

 

[henry_m]

Here's an interesting question inspired by discord's post: suppose we have a positively charged particle and a positively charged conducting sphere. We hold the charge a little off centre and let all the charges in the sphere settle down (so it's just electrostatics), and then let it go. Does the charge move back to the centre or go off and hit the sphere?

If the sphere is uncharged, I think it's fairly clear that it will be the latter. After a little thought I'm convinced that if the charge on the sphere is high enough, it will be the former. But at what ratio does the behaviour change?

(Easier warm up: what if we work in 2D, so the sphere becomes a long cylinder, and the point charge a charged rod? Complex variables make life better here.)

 

[Discord7]

Here's an interesting question inspired by discord's post: suppose we have a positively charged particle and a positively charged conducting sphere. We hold the charge a little off centre and let all the charges in the sphere settle down (so it's just electrostatics), and then let it go. Does the charge move back to the centre or go off and hit the sphere?

If the sphere is uncharged, I think it's fairly clear that it will be the latter. After a little thought I'm convinced that if the charge on the sphere is high enough, it will be the former. But at what ratio does the behaviour change?

Within an uncharged sphere, a single charged particle should drift aimlessly. Two or more particles of exclusive polarity would repel each other to the outer surface if able to travel, else would induce equal and opposite charge upon the inside surface of a hollow conductive shell. Barring conductance to the outer shell, a macroscopic neutrality would have to persist. Ergo, gain or loss of charged particles at inner surface presents a corresponding and respective loss or gain upon outer surface. All particles of the excess polarity thus either travel or propagate to the outer surface.

For a charged sphere, any insertion of a charged particle of matching polarity produces outward travel or propagation. (There is no penalty for just being late to join the others.) Any inserted charge less than the charge upon the sphere and of opposite polarity would descend to the center of the sphere. Certainly, anything that pulls one polarity will push the other one.

 

[Dale]

If you place a charge +q at the exact center of a conducting sphere, will it stay there or move to the surface?

It will spread out and distribute itself evenly across the surface regardless of the charge already there. It will not be in any kind of equilibrium in the center.

 

[Idoubt]

thx for the replies everyone, that does make it much clearer.