Consider an uncharged sphere, made of electrically conducting material. We then charge the sphere with excess charges.

I understand that these excess charges repel each other till the electric field lines parallel to the surface of the sphere cancel out. Each charge experiences the superposition of electric fields provided by all other charges, and no net force is exerted on any charge. This results in an evenly distributed charge distribution on the surface of the sphere.

The system is in stable electrostatic equilibrium.

Consider that we take the same sphere with all the excess charges on the surface, and insert an additional charge into the center of the sphere, such that the system is in unstable electrostatic equilibrium.

Is this particular distrubution of charges (including the center charge) the only configuration of unstable electrostatic equilibrium?

Put another way, other than the distributions above, is there no other configuration of charges such that the closed system is in unstable electrostatic equilibrium?

Why yes/no?

  • $\begingroup$ A charge placed at the center will be innunstable equilibrium. I did not get your question. $\endgroup$ – Lelouch Jan 24 '17 at 4:06
  • $\begingroup$ Perhaps it should be neutral equilibrium? $\endgroup$ – Farcher Jan 24 '17 at 7:09
  • $\begingroup$ Farcher, I assume you're talking about the sphere with surface charges and center charge? I would think it's unstable, because any deviation from center results in a nonzero superposition of electric field vectors (considering distances to each equally distributed surface charge), hence a nonzero force on the center charge, and movement away from equilibrium. But I'm wondering if we can achieve at least one other equilibrium (of any kind: stable, neutral, or unstable) by using any amount of charges, and placing them anywhere in the sphere. $\endgroup$ – Zhengqun Koo Jan 24 '17 at 7:20

In an electrostatic situation, any net charge on a conductor resides on the surface as this is the configuration that minimizes the potential energy of the system. With a single charge, there are infinitely many configurations that minimize the potential energy - every configuration has the same potential energy. So in that sense, the charge is neither in a stable nor unstable equilibrium. It's PE would be constant as a function of position (but infinite outside of the conductor).

That's the classical version. In modern theory, the charge will never stay still in such a situation.

This is just my take on it. Please correct me if anyone finds any error in this or if I may have misunderstood the question.

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