While it may seem obvious, it bears saying that the electric
fields due to several different "source" charges
or the magnetic fields due to several different "source"
current elements are just added together (vectorially, of course)
to make the net 
or 
field.
Horrible as it might seem, this might in principle not
be true - we might have to "add up" such fields in some
hopelessly more complicated way. But it didn't turn out
that way in this universe. Lucky us!