A charge of +3q is placed at the center of an unchanged conducting shell. What will be the charges on the inner and outer surfaces of the shell, respectively?
A. -3q, +3q
B. -3q, +6q
C. -3q, -3q
D. -q, +q
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More intuitively perhaps, a charge brought near a conductor induces in the conductor a charge of opposite sign closest to the charge. So the inside of the sphere should have an induced charge which is negative, because +3q is positive.
Now, the exterior must be the opposite of whatever is in the interior. Hence its sign is +.
Therefore option A or D is correct. Now the only question is whether you think that induced charge will have the same magnitude or not?
same hence shell is uncharged
just use the gauss theorem here. Take a closed spherical Gaussian surface with lie within the thickness of conducting shell. Since the electric field inside the conductor is zero here, so according to gauss law which is \[closed \int\limits E.dS = q(enclosed)/\epsilon\] . Since E is zero q enclosed must also be zero, so to do that charges(-3q here) from conducting shell comes to the inner side to make the net charge inside that gaussian surface zero.. And also due to conservation of charge , on the outer side +3q develops.