Chapter 20, Problem 59A

To determine

Charge on the second sphere.

Answer to Problem 59A

  $q_2=1.633\times {10}^{-8}\text{C}$

Explanation of Solution

Given:

Charge on first sphere, $q_1=3.6\times {10}^{-8}\text{C}$

Distance between the spheres, $d=1.4\text{cm}=0.014\text{m}$

Force experience, $F=2.7\times {10}^{-2}\text{N}$

Formula Used:

From Coulomb’s law,

  $F=\frac{K{q}_1{q}_2}{d^2}$

Where,

  $F$ is electrostatic force

  $K$ is coulomb’s constant

  $q_1$ and $q_2$ are charges and

  $d$ is distance between the charges.

Calculation:

As, $K=9\times {10}^9\text{N}{\text{.m}}^2/{\text{C}}^2$

On putting the values,

  $\begin{array}{c}2.7\times {10}^{-2}=\frac{9\times {10}^9\times \left(3.6\times {10}^{-8}\right)\times \left(q_2\right)}{{\left(0.014\right)}^2}\\ q_2=\frac{2.7\times {10}^{-2}\times {\left(0.014\right)}^2}{9\times {10}^9\times \left(3.6\times {10}^{-8}\right)}\\ =1.633\times {10}^{-8}\text{C}\end{array}$

Conclusion:

Therefore, the charge on the second sphere is $q_2=1.633\times {10}^{-8}\text{C}$ .