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## Homework Statement

J = ne(v). (yes. it's a vector equation and I haven't indicated that, but just ignore that. It's not important to my question.)

Let's say you have some positive ions traveling downward, and some negative ions traveling upward. The electric field is downward. Let's say you also know J. You know n, the number of carriers per unit volume for the positive ions and negative ions (which need not be the same n for each one).

To solve for v, it's pretty clear that you simple need to do: J/ne.

One of the things that is tripping me up is that I'm supposed to know that n here equals:

n (for the positive ions) PLUS n (for the negative ions).

An equivalent statement (and supposed to be explanation) is that: The positive and negative singly charged ions have drift velocities in opposite directions, so their current densities ADD.

But I don't get it. Why do they add and not subtract? Secondly, when would they subtract?