What is the net electric flux through the torus (i.e., doughnut shape) of FIGURE ?

The number of powerlines of force (or electrostatic force) that intersect a given area is that the property of an electrical field called electric flux. Field of force lines are thought to start with positive electric charges and end with negative ones.

The amount of electrical field that travels through a closed surface is remarked because the electrical flux. The electrical flux across a surface is proportional to the charge inside the surface, per Gauss's law.

$$\begin{gathered} {\Phi }_{\mathrm{e}}=\oint \overrightarrow{E}·d\overrightarrow{A} \\ =\frac{Q_{\text{in}}}{{ϵ}_o} \end{gathered}$$

The electric flow is set by the charge inside the closed surface, as indicated. Outside the closed surface, any flux to charges is zero, hence find the flux outside the gaussian exterior. The inert force could a charge that has no effect on the body.

$$\begin{gathered} Q_{\text{in}}=(-1\mathrm{nC})\left(\frac{1\times {10}^{-9}\mathrm{C}}{\mathrm{nC}}\right) \\ =-1\times {10}^{-9}\mathrm{C} \end{gathered}$$

Put the values,

${\Phi }_{\mathrm{e}}=\frac{Q_{\mathrm{in}}}{{ϵ}_o}$

$=\frac{-{10}^{-9}\mathrm{C}}{8.85\times {10}^{-12}{\mathrm{C}}^2/{\mathrm{Nm}}^2}$

$=-113{\mathrm{Nm}}^2/\mathrm{C}$