Chapter 16, Problem 7P

To determine

The distance between the charged spheres when they are moved.

Answer to Problem 7P

The distance between the charged spheres is $4.87\text{cm}$ .

Explanation of Solution

Given:

The initial distance between the charged spheres is $8.45$ centimeters.

Formula used:

Let the magnitude of the first charged sphere is $Q_1$ and the magnitude of the second charged sphere is $Q_2$ . The initial distance between the charged sphere is $r$ .

Write the expression to calculate the magnitude of force acting between two charged sphere using Coulomb’s law.

  $F=k\frac{Q_1{Q}_2}{r^2}$.... (1)

Where,

The force acting between two charged spheres is $F$ .

The Coulomb’s constant is $k$ and its value is $8.988\times {10}^9\text{N}\cdot {\text{m}}^{\text{2}}{\text{/C}}^2$ .

Calculation:

From equation (1), the force is inversely proportional to the square of the distance between charged spheres.

  $F\propto \frac{1}{r^2}$

From the above, it is clear that force is decreased by a factor of $\sqrt{3}$ when the force is tripled.

Calculate the distance between the charged spheres when they are moved.

  $\begin{array}{c}\text{Distance}=\frac{8.45}{\sqrt{3}}\\ =4.87\text{cm}\end{array}$

Conclusion:

Therefore, the distance between the charged spheres is $4.87\text{cm}$ .