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A metal cube of side 5 cm is charged with $6\ \mu C$. The surface charge density on the cube is
A
$0.125\times10^{-3}\ C\,m^{-2}$
B
$0.25\times10^{-3}\ C\,m^{-2}$
C
$4\times10^{-3}\ C\,m^{-2}$
D
$0.4\times10^{-3}\ C\,m^{-2}$
Detailed Solution
In a metal, all charge resides on the surface. $Q=6\ \mu C$. Total surface area $A=6a^2=6\times(5\times10^{-2})^2=150\times10^{-4}\ m^2$. Surface charge density $\sigma=\dfrac{Q}{A}=\dfrac{6\times10^{-6}}{150\times10^{-4}}=0.4\times10^{-3}\ C\,m^{-2}$.