Three concentric spherical shells of radii r1 r2 r3 have charges
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Consider a Gaussian surface (dashed black circle) lying inside the shell C.
In a conductor electric field is zero in static conditions. The net flux through our chosen Gaussian surface is therefore zero. According to Gauss’s theorem, the surface must enclose no net charge. Since +3Q (+Q on shell A and +2Q on shell B) charge exists inside it, -3Q charge must induce on the inner surface of the shell C and consequently +3Q on the outer surface of C. Since -Q charge is already there on the outer surface of C, the net charge there is -Q + 3Q = +2Q.
Note that there is no need to know how the charge on the inner shells is distributed. However if you are interested to know this you can choose another Gaussian surface inside the shell B and proceed in the similar manner.
In a conductor electric field is zero in static conditions. The net flux through our chosen Gaussian surface is therefore zero. According to Gauss’s theorem, the surface must enclose no net charge. Since +3Q (+Q on shell A and +2Q on shell B) charge exists inside it, -3Q charge must induce on the inner surface of the shell C and consequently +3Q on the outer surface of C. Since -Q charge is already there on the outer surface of C, the net charge there is -Q + 3Q = +2Q.
Note that there is no need to know how the charge on the inner shells is distributed. However if you are interested to know this you can choose another Gaussian surface inside the shell B and proceed in the similar manner.
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