Chapter 20, Problem 33A

To determine

To Explain:Whether Bernoulli would have found the dependence of strength of electrostatic force on distance between the two close charged metal disks as $\frac{1}{r^2}$ or not.

Answer to Problem 33A

No

Explanation of Solution

Introduction:

Electrostatic force between two charges can be obtained by:

$F=k\frac{q_1{q}_2}{r^2}$

Here, k is the Coulomb’s constant, $q_1$ and $q_2$ are two charges and ris the distance between them.

The dependence of distance as $\frac{1}{r^2}$ is valid only when the two charged bodies are actually point particles or which can be approximated as one. Since the distance between the metal disks is small, they cannot be treated as point particles and hence, the inverse square law would not be derived in the Bernoulli’s experiment. The metal disk can be considered as a group of charged point particles and to find the dependence of electric force, it must be integrated over entire disk.

Conclusion:

Thus, Bernoulli would not have found the dependence of strength of electrostatic force on distance between the two close charged metal disks as $\frac{1}{r^2}$ or not.