SCN3797-ABED_1: 7.1 Gravitation and Electrostatics

Charles de Coulomb, in 1785, investigated the precise relationship between electrostatic forces and distance of separation. Coulomb was a former military engineer. He used his engineering skills to design and build a precision device to explore the variables that affect electric forces. The results of his work provide a precise description of the electric force that exists between two charged objects separated by a known distance.

Coulomb did not begin his work on determining the electric force law on his own. As the following timeline indicates, other scientists had already done much of the essential groundwork. You might be surprised to know that the essential ideas came from Isaac Newton's work on gravitation.

Image by Comfreak from Pixabay

Date	Scientist	Contribution to Coulomb's Work
1687	Isaac Newton	Published his great book Mathematical Principles of Natural Philosophy , which included his three laws of motion and his law of universal gravitation: $\|{\vec{F}}_{g}\| = \frac{G m_{1} m_{2}}{r^{2}}$
1775	Benjamin Franklin	Franklin noticed that a small cork inside a hollow, charged can experiences no force. The same cork experiences a force outside the can. He wrote to Joseph Priestly and asked him to repeat the experiment.
1776-1777	Joseph Priestley	Priestley verified Franklin's results and realized a connection to Newton's law of universal gravitation. Newton had explained in his book that an object would experience no force of gravity inside a hollow planet. He was able to show that this was the consequence of the "inverse squares law," which says that gravitational force acting on two masses is inversely proportional to the square of the distance between their centres. Priestly instantly likened the cork to the object and the hollow can to the planet. Priestley suggested that this indicated that the force of electricity could also be an inverse square law.

Date

Scientist

Contribution to Coulomb's Work

1687

Isaac Newton

Published his great book Mathematical Principles of Natural Philosophy , which included his three laws of motion and his law of universal gravitation:

$|{\vec{F}}_{g}| = \frac{G m_{1} m_{2}}{r^{2}}$

1775

Benjamin Franklin

Franklin noticed that a small cork inside a hollow, charged can experiences no force. The same cork experiences a force outside the can. He wrote to Joseph Priestly and asked him to repeat the experiment.

1776-1777

Joseph Priestley

Priestley verified Franklin's results and realized a connection to Newton's law of universal gravitation. Newton had explained in his book that an object would experience no force of gravity inside a hollow planet. He was able to show that this was the consequence of the "inverse squares law," which says that gravitational force acting on two masses is inversely proportional to the square of the distance between their centres.

Priestly instantly likened the cork to the object and the hollow can to the planet. Priestley suggested that this indicated that the force of electricity could also be an inverse square law.

Read Coulomb's Law

To review the key features of Newton's law of universal gravitation and to better understand what it means to say that this law is an "inverse square law," read page 524. Pay special attention to the "Physics Insight" on the left-hand side of the page.

Self-Check 1

List all the variables that influence the magnitude of the force of gravity.

Suggested Answer

The magnitude of the force of gravity is affected by the mass of the two objects and the distance between their centres.

Self-Check 2

Describe how increasing the size of both masses influences the magnitude of the force of gravity.

Suggested Answer

As the masses increase, the force increases. This is a direct relationship.

Self-Check 3

Describe how increasing the distance ( r ) between the two masses influences the magnitude of the force of gravity $|{\vec{F}}_{g}|$

Suggested Answer

As the distance ( r ) between the two masses increases, the magnitude of the force of gravity $|{\vec{F}}_{g}|$ decreases. This is an inverse square relationship.

Self-Check 4

Mathematically express how increasing the size of both masses influences the magnitude of the force of gravity. In other words, write a proportionality statement.

Suggested Answer

$|{\vec{F}}_{g}| α m_{1} m_{2}$

Self-Check 5

Mathematically express how increasing the distance ( r ) between the two masses influences the magnitude of the force of gravity. In other words, write a proportionality statement.

Suggested Answer

$|{\vec{F}}_{g}| α \frac{1}{r^{2}}$

Try This

Given your answers to the previous questions, you should be able to speculate about the nature of the electrostatic force. The following graphic shows the possible connections between the gravitational force acting on two masses ( m₁ and m₂ ) and the electrostatic force

|{\vec{F}}_{e}|

acting on two charges ( q₁ and q₂ ).

$|{\vec{F}}_{g}| = \frac{G m_{1} m_{2}}{r^{2}}$

|{\vec{F}}_{e}| = ?