Electric Potential, Max/Min and Stability?

Question

I'm not really sure how to go about this Physics Problem.

An electrostatic potential has a maximum at point P and a minimum at point M. Are either (or both) of these points equilibrium points for a negative charge? If so are
they stable? What about for a positive charge?

That is all that is stated in the problem.
Thanks

Answer 1

If a slight displacement from the position results in a net force component against the displacement, it's stable. If the net force is zero or perpendicular to the displacement it's neutrally stable. If it has a component in the direction of the displacement it's unstable.
A maximum + (or minimum -) potential has a negative gradient in all directions so is stable for a - charge. A minimum + potential (or a maximum - potential) has a positive gradient in all directions so is stable for a + charge. For a sign change of either one or three but not two of: the potential, the charge, or the maximum/minimum description; the points are unstable.

Answer 2

electric powered ability is a level of the means of an electric powered container to do paintings, in protecting with unit charge (dV = -W/dq) it might want to be analagous to the aptitude of an merchandise intense in a gravitational container, because this is going to have a tendency to a decrease element, so does electric powered charge, this is going to go back and forth from intense to low ability (common present day, electrons actual go back and forth the option way). This vast difference of ability is ability vast difference, or Voltage. EMF or electro purpose rigidity, is the rigidity responsible for shifting charge via a circuit (providing present day), and is the optimum ability vast difference for the length of a circuit (i.e even as it isn't closed, is an same as terminal voltage), even as a circuit is closed, emf drops by way of terminal resistance of EMF source (battery and so on) expenses flow by utilizing the action of loose electrons interior the metal