I know that different points can have the same potential energy. But is the opposite possible?

(i.e. can the same point have different potential energies?)

(The reference point for zero potential energy is fixed)

I think the answer is no.

But, then I don’t understand how any of these is possible

enter image description here

  • $\begingroup$ Could you give some context about this graph? What is shown, where is it from etc? $\endgroup$ May 22 at 7:48
  • $\begingroup$ @CharlesTucker3 V represents potential energy and the graph shows the variation of V with position x $\endgroup$ May 22 at 7:50
  • $\begingroup$ What part of which graph is it that you see confusion for? A point is only associated with one potential energy value (for a fixed reference point) at any moment just like it is only associated with, say, one position, one charge value, one temperature etc. $\endgroup$
    – Steeven
    May 22 at 7:55
  • $\begingroup$ @CharlesTucker3 That means the graphs are wrong, correct? $\endgroup$ May 22 at 7:56
  • $\begingroup$ The question was to choose from 4 options which are possible. $\endgroup$ May 22 at 7:57

A potential is a scalar field, having a value at points in space. It is not well-defined for such a field to have multiple values at a single point, so for electric potential it is safe to say no, you cannot have two values at a single point. It is possible, though, to define a gravitational potential as well as an electric potential; the two different fields can be defined over the same space, but would not carry the same values.

Potential 'steps' are likely just steep slopes; an infinite voltage gradient, for example, means infinite electric field, which is not realistic, nor compatible with normal matter composed of atoms...

The familiar square well potentials of quantum mechanics are... soluble mathematically, but not entirely realistic, either.


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