Chapter 16, Problem 52GP

To determine

To Find: The least distance between two electrons .

Answer to Problem 52GP

5.08 m

Explanation of Solution

Given:

Electric force between two electron is equal to the weight of the electron that is ${\mathrm{F}}_{\mathrm{E}}={\mathrm{F}}_{\mathrm{G}}$

Formula used:

  $\mathrm{k}\frac{{\mathrm{e}}^2}{{\mathrm{x}}^2}=\mathrm{m}\mathrm{g}$

Where,

  $\mathrm{e}=$ charge on electron

  $\mathrm{m}=$ mass of electron

  $\mathrm{g}=$ acceleration due to gravity

Calculation:

Let the separation between the electrons be ‘x’

Electric force = weight of electron

  $\begin{array}{l}\mathrm{k}\frac{{\mathrm{e}}^2}{{\mathrm{x}}^2}=\mathrm{m}\mathrm{g}\hfill \\ {\mathrm{x}}^2=\frac{\left(9.0\times {10}^9\right){\left(1.6\times {10}^{-19}\right)}^2}{(9.8)\left(9.1\times {10}^{-31}\right)}\mathrm{m}\hfill \\ {\mathrm{x}}^2=25.8\hfill \\ \mathrm{x}=5.08\text{m}\hfill \end{array}$

Conclusion:

Distance between electrons must be $=5.08\text{m}$