729 small identical spheres each charged to an electric potential 3V combine to form a bigger sphere. The electric potential of the bigger sphere is
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When N identical spheres of radius $r$ combine to form a single large sphere:
- The new radius is $R = N^{1/3}r$.
- The new charge is $Q = Nq$.
- The new potential is $V_B = N^{2/3}V_s$.
This power law relationship is a useful shortcut for such problems.