Current density and drift velocity

AI Thread Summary
The discussion centers on the relationship between current density (J), charge carrier density (n), and drift velocity (v) in a system with both positive and negative ions. It clarifies that the total carrier density n is the sum of the densities of positive and negative ions, which is crucial for calculating drift velocity. The current densities of positive and negative ions add together because they flow in opposite directions, contributing to the overall current. The confusion arises regarding when current densities would subtract instead of add, highlighting the need for further clarification on the conditions that lead to such scenarios. Understanding these principles is essential for solving related problems in electromagnetism.
auk411
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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?
 
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Look at your earlier thread.
 
SammyS said:
Look at your earlier thread.

I did and more responses are needed.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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