Chapter 21, Problem 28E

Interpret This problem involves applying Gauss's law to find the electric flux through a sphere that encloses a given charge.

Develop Gauss's law (liquation 21.3) states that the electric flux through a closed surface is proportional to the charge enclosed. Specifically,

$\Phi ={\displaystyle \oint \bar{E}}\cdot \overline{dA}=q_{\frac{enclosed}{{\epsilon }_0}}$

so given q_enclosed, we can find $\Phi$.

Evaluate The electric flux is

$\frac{q_{enclosed}}{{\epsilon }_0}=\frac{\left(6.8-4.7\right)\mu C}{8.85\times {10}^{-12}{C}^2/\left(N\cdot m^2\right)}=240\text{ k}N\cdot m^2\text{/C}$

  28. A 6.8-μC charge and a −4.7-μC charge are inside an uncharged sphere. What's the electric flux through the sphere?