Question

A cube of side 5 cm has a charge of 6 $\mu$C . The surface charge density in $C/m^2$ is

• A. $4\times {10}^{-2}$
• B. $4\times {10}^{-4}$
• C. $4\times {10}^{-6}$
• D. $4\times {10}^{-8}$

Answer 1

The correct option is B $4\times {10}^{-4}$

$\text{Step 1: Surface charge density}$

Given, Total Charge on cube $q=6\mu C$

Side of Cube$,a=0.05m$

As cube has $6$ square faces, so its total surface area $=6a^2$

Surface charge density $=\frac{\text{Total Charge}}{\text{Surface area}}$ $=\frac{q}{6a^2}$

$=\frac{6\times {10}^{-6}C}{6\times (0.05m{)}^2}$

$=4\times {10}^{-4}C/m^2$

Hence, Correct option is $B$