A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R=n$$ $$r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

Question

Infinity Learn · Accepted Answer

Let say inside shell has charge $$q1$$ and outside shell has charge $$q2$$.​Surface charge densities are equal for both shells.​⇒$$q14$$$$π$$$$r2=q24$$$$π$$$$R2$$ ⇒$$q1q2=r2R2$$→$$1$$​  &​ $$q1+q2=Q$$→$$2$$​∴$$q1=r2r2+R2Q$$    &    $$q2=R2R2+r2QPotential$$ at common centre $$=$$ $$V=Kq1r+Kq2R=KQrr2+R2+KQRR2+r2=KQr+Rr2+R2=KQr+nrr2+nr2=KQ1+nr1+n2$$

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R=n r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

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