Chapter 17, Problem 23P

To determine

The work done will be calculated.

Answer to Problem 23P

The answer is $6.9\times {10}^{-18}\text{J}$ .

Explanation of Solution

Given data:

Distance, $L=1.0\times {10}^{-10}m$

Formula used:

It is known that: $W=\frac{k{e}^2}{L}$

Where,

  $W$ is the work done.

  $\text{e}$ are electric charge.

  $k$ is the constant factor.

  $\text{L}$ is the distance between two charges.

Calculation:

Let an equilateral triangle whose sides are $\text{L}$ in length. Then the work done for three electrons is ${\text{W=W}}_{\text{1}}{\text{+W}}_{\text{2}}{\text{+W}}_{\text{3}}$

Substitute the data, ${\text{W=W}}_{\text{1}}{\text{+W}}_{\text{2}}{\text{+W}}_{\text{3}}$

  $\text{W}=0+\frac{{\text{ke}}^2}{\text{L}}+\frac{{\text{2ke}}^2}{\text{L}}$

  $\text{W}=\frac{{\text{3ke}}^2}{\text{L}}$

  $\text{W}=\frac{\text{3}\left(8.99\times {10}^9\text{N}\cdot {\text{m}}^2/{\text{C}}^2\right)\left(1.60\times {10}^{-19}\text{C}\right)}{\left(1.0\times {10}^{-19}\text{m}\right)}$

  $\text{W}=6.9\times {10}^{-18}\text{J}$

Conclusion: The total work done is $6.9\times {10}^{-18}\text{J}$ .