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Robert Israel
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Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT: Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$. By time $t=40$, all but four had managed to escape the cage. An animation of the trajectories is here. The last one escaped by $t=70$.

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT: Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$. By time $t=40$, all but four had managed to escape the cage. An animation of the trajectories is here.

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT: Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$. By time $t=40$, all but four had managed to escape the cage. An animation of the trajectories is here. The last one escaped by $t=70$.

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Robert Israel
  • 54.2k
  • 1
  • 76
  • 152

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT: Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$. By time $t=40$, all but four had managed to escape the cage. An animation of the trajectories is here.

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.

EDIT: Just for fun, I tried it numerically using $60$ unit charges at the vertices of a truncated icosahedron, with $100$ randomly chosen initial velocities with speed $0.01$. By time $t=40$, all but four had managed to escape the cage. An animation of the trajectories is here.

Source Link
Robert Israel
  • 54.2k
  • 1
  • 76
  • 152

Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the origin within your "cage". Therefore it is impossible to do what you want: there will always be a path the electron can take to escape to infinity.