Chapter 26, Problem 70A

To determine

The force between the two spheres when they are touched together.

Answer to Problem 70A

The force between the two spheres when they are touched together is $F^{\text{'}}=\frac{1}{8}F$ .

Explanation of Solution

Given info:

The values are

  $\begin{array}{l}{q}_1=-4q\\ q_2=+2q\end{array}$

Formula used:

The formula is given by,

  $F=\frac{K\times q_1\times q_2}{r^2}$

Calculation:

According to the equation

  $\begin{array}{c}F=\frac{K\times q_1\times q_2}{r^2}\\ F=\frac{K\times 4q\times 2q}{r^2}\\ F=\frac{8K{q}^2}{r^2}\end{array}$

The total charge on the sphere is

  $\begin{array}{c}{q}_{net}=q_1+q_2\\ =-4q+2q\\ =-2q\end{array}$

After connecting the spheres charges on each of the spheres is the half of the $q_{net}$

  $\begin{array}{c}{q}_1{}^{\text{'}}=q^{\text{'}}{}_2\\ =-q\end{array}$

The fore between them:

  $\begin{array}{l}{F}^{\text{'}}=\frac{K\times q_1\times q_2}{r^2}\\ F^{\text{'}}=\frac{K\times q^2}{r^2}\\ F^{\text{'}}=\frac{1}{8}F\end{array}$

Conclusion:

Hence, the force between the two spheres when they are touched together is $F^{\text{'}}=\frac{1}{8}F$ .