- #26

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You can add them if you set them to be zero "outside of their domain". But then it is obvious that the equation doesn't hold in all points e.g in a point ##r_2## of the domain of ##J_2## where ##\vec{J_2}(\vec{r_2})\neq\vec{0}## but ##\vec{J}(\vec{r_2})=\vec{J_1}(\vec{r_2})=\vec{0}##In order to add them, ##\vec {j_1}## and ##\vec {j_2}## must be evaluated at the same point. How can you do that when they’re in different wires or resistors?

I believe that my example at post #24 shows that even in the junction point that is common to the domain of all three, the equation doesn't necessarily hold.