We deal here with the equilibrium of parallel metallic conductors .
The axis of conductors are perpendicular to the screen . The electric field is zero inside the conductor and there are charges only at their outer surface.
The electric field is , just outside of these, on the one hand perpendicular to the surface and on the other hand proportional to the charge density at local surface. The surface charge density can therefore be indicated by the fields at the exit of conductoers, and this is what is done here. The charges are positive for emerging fields from the conductor, negative for entering those .
These properties are enough to determine the electrical fields throughout the space , once known total charge per unit length of each cylindrical conductor.
We consider the case of N conductors ( N < = 4) , whether or not located inside a « wrapping » hollow conductor and whose charge is opposite to the sum of the charges of then N conductors ( to satisfy the Gauss theorem ); this « wrapping » conductor is actually always present, but situated at infinity , which allows the total nullity charges . The radii of the conductors , their positions and their charges can be varied at will .
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