Question

Use Coulomb's law,

$$\begin{gathered} \mathit{V}\mathbf{=}\frac{{\mathbf{Q}}_{\mathbf{1}}{\mathbf{Q}}_{\mathbf{2}}}{\mathbf{4}\mathbf{\pi }{\mathbf{o}}_{\mathbf{0}}\mathbf{r}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{31}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{19}}\mathit{J}\mathit{n}\mathit{m}\left(\frac{Q_1{Q}_2}{r}\right) \end{gathered}$$

to calculate the energy of interaction for the following two arrangements of charges, each having a magnitude equal to the electron charge.

(a)

(b)

Short answer

Answer:

(a)$V\mathit{=}\mathit{-}\mathit{4}\mathit{.}\mathit{62}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{18}}J$

(b) $\mathrm{V}=-5.98\times {10}^{-18}\mathrm{J}$

Step-by-step solution

CalculateV in part (a) for two attractions:

(a) In this situation, these will betwo attractions of type$\frac{\left(+1\right)\left(-1\right)}{\mathrm{r}}$

So,

$$\begin{gathered} V\mathit{=}\mathit{2}\mathit{\times }\left(2.31\times {10}^{-19}Jnm\right)\left[\frac{\left(+1\right)\left(-1\right)}{0.1nm}\right] \\ \mathit{}\mathit{}\mathit{=}\mathit{-}\mathit{4}\mathit{.}\mathit{62}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{18}}J \end{gathered}$$

Check the attractions in part (b):

(b) There will be4 attractionsin which $\left(+1\right)$and $\left(-1\right)$charges are separated by $1\times {10}^{-10}$or $0.1\mathrm{nm}$ from each other. Apart from that, there are 2 negative charges and positive charges repelling each otherdiagonally at a distance at $\sqrt{2}\times nm$.

So,

$$\begin{gathered} V\mathit{=}\mathit{4}\mathit{\times }\left(2.31\times {10}^{-19}Jnm\right)\left[\frac{\left(+1\right)\left(-1\right)}{0.1nm}\right]\mathit{+}\mathit{2}\mathit{.}\mathit{31}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{19}}Jnm\left[\frac{\left(+1\right)\left(-1\right)}{\sqrt{2}\left(0.1\right)nm}\right] \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{+}\mathit{2}\mathit{.}\mathit{31}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{19}}Jnm\left[\frac{\left(-1\right)\left(-1\right)}{\sqrt{2}\left(0.1\right)nm}\right] \\ V\mathit{=}\mathit{-}\mathit{9}\mathit{.}\mathit{24}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{18}}J\mathit{+}\mathit{1}\mathit{.}\mathit{63}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{18}}J \\ \mathit{}\mathit{}\mathit{=}\mathit{-}\mathit{5}\mathit{.}\mathit{98}\mathit{\times }{\mathit{10}}^{\mathit{-}\mathit{18}}J \end{gathered}$$