Question

The surface density of charge on the spherical surface is $2.65\times {10}^{-9}C/m^2$. If the radius of the sphere is $6.4\times {10}^6/m$, find the charge carried by the sphere.

Answer 1

Surface charge density ($\sigma$) $=2.65\times {10}^{-9}C/m^2$

Radius of sphere ($R$) $=6.4\times {10}^{6}m$

Area of sphere ($A$) $=4\pi r^2$

$\begin{array}{c}=4\times \frac{22}{7}\times {\left(6.4\times {10}^6\right)}^2\\ =514.719\times {10}^{12}{m}^2\end{array}$

Since, $\sigma =\frac{Q}{A}$

$\begin{array}{c}\Rightarrow Q=\sigma \times A\\ =2.65\times {10}^{-9}\times 514.719\times {10}^{12}\\ =1364.005\times {10}^3\\ Q=1.36\times {10}^{6}C\end{array}$