(*) Charge density is proportional to the Laplacian of this in Poisson's equation.
For a thermionic diode, the Child-Langmuir law says current density is proportional to this quantity to the three-halves power. It can be found numerically via a nearest neighbors sum with a fourth order Taylor expansion in the relaxation algorithm. The fact that, in free space, this quantity can only have a saddle point in interior regions leads to the inability of point charges to remain in static equilibrium or Earnshaw's theorem. In the Lorenz gauge, the divergence of the magnetic vector potential is set equal to the time derivative of this divided by the speed of light squared. (*) Charge density is proportional to the Laplacian of this in Poisson's equation. It is constant in a conductor and is generally set to zero at infinity. In electrostatics, its negative gradient gives the electric field. Multiplied by charge, it gives potential energy. For 10 points, name this scalar quantity whose difference is measured in volts.
For a thermionic diode, the Child-Langmuir law says current density is proportional to this quantity to the three-halves power.
Electric Potential [prompt on partial answers; prompt on V or voltage]