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50. A solid spherical conducting shell has inner radius a and outer radius 2a. At the center of the shell is located a point charge +Q. What must the excess charge on the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

I reasoned that the charge on the inner surfaces of the shell is -Q because the electrons are attracted towards the point charge. Thus the charge on the outer shell is +Q. The surface area of the outer shell is [tex]16\pi a^2 [/itex] and the surface are of the inner shell is [tex] 4\pi a^2 [/itex]. So the charge density on the outer is shell is [tex]\frac{Q}{16\pi a^2} [/itex] and the charge denisty on the inner shell is [tex]\frac{-Q}{4\pi a^2} [/itex]. So in order to make the charge density equal you need to add -5Q to the shell so that that charge accumulates outside and yields a charge density on the outer surface of [tex]\frac{-Q}{4\pi a^2} [/itex]. So the answer is -5Q which is also the answer according to the answer key, however my physics teacher does not agree. Is my reasoning correct cause I have to agrue this with him tommorow. Thanks