91影视

According to the Coulomb鈥檚 law, the force between two charges spaced at a distance is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.

Mathematically,

$\mathbf{F}\mathbf{=}\mathbf{k}\frac{\left|q_1{q}_2\right|}{{\mathbf{r}}^{\mathbf{2}}}$ 鈥�.. (1)

Here, F is the force, ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$are the charges, k is the Coulomb鈥檚 charge, and is the distance between two charges.

Consider the given data as below.

The repulsive force, $\mathrm{F}=3.33脳{10}^{-21}\mathrm{N}$

The Coulomb鈥檚 constant, $\mathrm{k}=9脳{10}^9\mathrm{N}路{\mathrm{m}}^2/{\mathrm{C}}^2$

The distance between charges, $\mathrm{r}=20\mathrm{cm}=2.0\mathrm{m}$

Rewrite equation (1) as below.

$$\begin{gathered} \mathrm{F}=\frac{{\mathrm{kq}}^2}{{\mathrm{r}}^2} \\ \left|\mathrm{q}\right|=\sqrt{\frac{{\mathrm{Fr}}^2}{\mathrm{k}}} \end{gathered}$$

Substitute known values in the above equation, and you have

$$\begin{gathered} \left|\mathrm{q}\right|=\sqrt{\frac{\left(3.33脳{21}^{-21}\mathrm{N}\right){\left(0.200\mathrm{m}\right)}^2}{9脳{10}^9\mathrm{N}.{\mathrm{m}}^2/{\mathrm{C}}^2}} \\ =1.217脳{10}^{-16}\mathrm{C} \end{gathered}$$

The charge of one electron is$1.6脳{10}^{-19}\mathrm{C}$.

Thus, the number of electrons on each sphere is,

$$\begin{gathered} n=\frac{\left|q\right|}{e} \\ =\frac{\left(1.217脳{10}^{-16}\mathrm{C}\right)}{\left(1.6脳{10}^{-19}\mathrm{C}/\mathrm{electron}\right)} \\ =760\mathrm{electron} \end{gathered}$$

Hence, there are 760 excess electrons on each sphere causing them to be negatively charged and repel each other.