Question

An electric charge can be held in a position of stable equilibrium
a) by a purely electrostatic forces
b) by purely a mechanical force
c) neither of the above
d) unpredictable​

Answer 1

Answer:

(a) no will be the answer

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Answer 2

a) By a purely electrostatic force

A charged particle will always move in one direction along a field line, while a positive particle will always move in the opposite direction. Converging field lines like these would be required to achieve a point of stable equilibrium: Field notations

As a result, the charged particle will be drawn to and held at the intersection of the lines, just like the red dot.

The problem is that the divergence at this point is non-zero, and Maxwell's equations tell us that a non-zero divergence requires the presence of some charge. As a result, you can't just create this field in the middle of your vacuum chamber.

Of course, you can create a similar field by filling your vacuum chamber with a significant charge.

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