Electrostatic-Conductive shells

[ivan314]

Homework Statement

There are 3 concentric conductive shells with radius 1R, 2R, and 3R and charges +Q,+Q,-2Q respectively find the electric field

Homework Equations

gauss law(electric flux)

The Attempt at a Solution

by gauss law
for an r<R E=0 because there is no charge

for R<r<2R E=+Q/(4*pi*r²*e₀)

for 2R<r<3R E=+Q/(4*pi*r²*e₀)

here is my question for 2R<r<3R is it right or is it like this
E=+Q/(4*pi*r²*e₀)+Q/(4*pi*s²*e₀)
where s is a radius 0<s<3R
I mean in the space 2R<r<3R does the field of the conductive shell with radius 1R affect here? or the field is affected just by the shell of radius 2R

and the same for 3R<r here the field is afected by all the shells or just by the one with radius 3R
thanks beforehand.

 

[anathema]

Hello, based on the given information, the electric field in the region 2R<r<3R will be affected by all three shells since they all have a non-zero charge. However, the contribution of the outer shell with a charge of -2Q will be greater compared to the other two shells. Therefore, the correct expression for the electric field in this region would be E = +Q/(4*pi*r2*e0) - 2Q/(4*pi*r2*e0) = -Q/(4*pi*r2*e0). Similarly, for 3R<r, the electric field will only be affected by the outermost shell with a charge of -2Q, so the expression for the electric field would be E = -2Q/(4*pi*r2*e0). I hope this helps clarify your doubts.