A metal cube has a uniform surface charge density of $1.5 \mu\mathrm{C} \mathrm{m}^{-2}$. If the sid

Question

A metal cube has a uniform surface charge density of $1.5 \mu\mathrm{C} \mathrm{m}^{-2}$. If the side length of the cube is $2 \mathrm{~cm}$, the total charge on the cube is

Professor PC Thomas Classes · Answer

(a) : The total surface area of a cube of side $l$ is $S = 6l^2$. Given $l = 2 \mathrm{~cm} = 0.02 \mathrm{~m}$, the area is $S = 6 	imes (0.02)^2 = 0.0024 \mathrm{~m}^2$. The total charge is the product of surface charge density ($\sigma$) and area ($S$). Thus, $Q = \sigma 	imes S = 1.5 	imes 10^{-6} 	imes 0.0024 = 3.6 	imes 10^{-9} \mathrm{C} = 3.6 \mathrm{nC}$.