Numerical and analytical verifications of the electrostatic attraction between two like-charged conducting spheres

• Like-charged spheres in proximity attract each other!
• Numerical and analytical electrostatic simulations verify this.
• The theoretical charge density profile is verified numerically.
• Practical implementations of the formulae are given.

We calculate the capacitance coefficients for the problem of two conducting spheres using a numerical (boundary element) method as well as two analytical approaches. The consistency of the results serves as an independent verification of the counter-intuitive analytical result that like-charged spheres almost always attract at close approach. We further support this claim by reproducing the analytical surface charge density with the numerical method. Practical implementations are given in the Supporting Information.

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