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The interraction between Charge and Field can be simplified into two logical statements:

1) If x

2) Then y

X is the charge, while Y is the field. 

X = positive, negative, and neutral.

Y = positive, negative, and neutral. 

We first check for the charge, and then for the field. 

a) As I said in the rules, only pieces of oposite charges can capture each other. Neutral pieces are not affected by these rules and can capture, or be captured by any piece. 

b) The above rule is only true on a positive or negative field. If the field where the capture happens is positive, the white piece remains on the board. If the field is negative, the black piece remains on the board. 

c) On a neutral field, the charge doesn't matter. 

I hope this is clear. 

Latter on, I'll make some example diagrams to explain the capturing mechanism.