Question

What is Electrostatic configuration???​

Answer 1

Answer:

Let the equilibrium of the test charge be stable. If a test charge is in equilibrium and displaced from its position in any direction, then it experiences a restoring force towards a null point, where the electric field is zero. All the field lines near the null point are directed inwards towards the null point. There is a net inward flux of electric field through a closed surface around the null point. According to Gauss's law, the flux of electric field through a surface, which is not enclosing any charge, is zero. Hence, the equilibrium of the test charge cannot be stable.

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Answer 2

Explanation:

Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. ... Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces.

So, I've been told by Earnshaws Theorem that it's impossible to trap a charged particle using an purely electrostatic configuration. However, this doesn't seem to make intuitive sense. If I were to create a sphere whose surface consisted purely of positive charges, evenly distributed over the surface and then placed a single positive charge in the middle, would that not be trapping a particle in an electrostatic configuration? There would even be a restoration force as if the particle was "nudged" slightly, the net force would be to push the particle back into the center. I'm mostly looking for an intuitive answer. Have I missed something? Is this not defined as electrostatic?

A mathematical explanation would also be appreciated alongside an intuitive one.