Why does moving a negative charge to a negative plate cause the potential difference to be negative?

[Padfoot]

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There's a problem asking to calculate the work that must be done to move a -2 coulomb charge from the positive plate to the negative plate of a capacitor charged to 10V. The explanation says "We are moving a negative charge to the negative plate (ie the lower potential plate). Therefore, both q and the potential difference are negative".

I'm confused as to why the negative plate is the "lower potential plate"? Is there a mathematic explanation for this?

 

[erythrocyte666]

V = kq/r --> b/c q is positive at positive plate, V is positive there; V is negative b/c q is negative at negative plate
delta V = Vfinal - Vinitial = negative since V initial was positive as I said above and Vfinal is negative.
Having said that, potential energy of the -2 C charge will increase in this process.