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 of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal ?
Medium
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$\frac{\mathrm{Q}+\mathrm{q}}{4 \pi(2 \mathrm{a})^{2}}=\frac{-\mathrm{Q}}{4 \pi \mathrm{a}^{2}}$
$\frac{\mathrm{Q}+\mathrm{q}}{4}=-\mathrm{Q}$
$\mathrm{Q}+\mathrm{q}=-4 \mathrm{Q}$
$q=-5 Q$
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