Question

A 5.0-cm-diameter metal ball has a surface charge density of $10mC/m2$. How much work is required to remove one electron from this ball?

Short answer

The work is needed to remove one electron from the ball is $-4.5\times {10}^{-15}J$

Step-by-step solution

Definition of potential charge 

The equation of the potential of a charge is

$V=1/\left(4\pi {\epsilon }_0\right)q/r$

as the charge is sphere so the $q=4\pi r^2\rho$

Applying the data $V=\frac{r\rho }{{\epsilon }_0}$

theory of work energy 

Removal one electron from the ball, the work needs

As $W=eV$$W=eV$

localid="1648302583389" $\begin{array}{rcl}& & \\ \rho & =& 10\mu C/m^2\\ {\epsilon }_0& =& 8.85\times {10}^{-12}{C}^2/N.m^2\\ e& =& 1.6\times {10}^{-19}C\\ r& =& 2.50cm\\ W& =& \frac{\left(1.6\times {10}^{-19}C\right)\left(2.50cm\right)\left(10\mu C/m^2\right)}{8.85\times {10}^{-12}{C}^2/N.m^2}\\ & =& -4.5\times {10}^{-15}J\end{array}$