Question

The form of Coulomb’s law is very similar to that for Newton’s law of universal gravitation. What are the differences between these two laws? Compare also gravitational mass and electric charge.

Short answer

The main difference between Coulomb’s law and Newton’s law of universal gravitation is that the former gives the expression for the electrostatic force between two charges, whereas the latter gives the expression for the gravitational force between two masses.

Step-by-step solution

Coulomb’s law and Newton’s law of gravitation

According to Coulomb’s law,the magnitude of force (F) that a small object (having charge${\mathbf{Q}}_{\mathbf{1}}$) exerts on another small object (having charge${\mathbf{Q}}_{\mathbf{2}}$) is directly proportional to the product of the charges on both objects and inversely proportional to the square of the distance (r) between them.

The expression for Coulomb’s force is:

$F=k\frac{Q_1{Q}_2}{r^2}$

Here, k is the electrostatic force constant.

According to Newton’s law of gravitation, the magnitude of force (F) that a small object (having mass${\mathbf{m}}_{\mathbf{1}}$) exerts on another small object (having mass${\mathbf{m}}_{\mathbf{2}}$) is directly proportional to the product of the masses of both objects and inversely proportional to the square of the distance (r) between them.

The expression for Newton’s law of gravitation is:

$F=G\frac{m_1{m}_2}{r^2}$

Here, G is the universal gravitational constant.

Differences between Coulomb’s law and Newton’s law of universal gravitation

• Coulomb’s law gives the expression for the electrostatic force between two charges, whereas Newton’s law of gravitation gives the expression for the gravitational force between two masses.
• The electrostatic force given by Coulomb’s law can be both attractive and repulsive in nature, while the gravitational force proposed by Newton’s law of gravitation always remains attractive.
• The magnitude of the electrostatic force given by Coulomb’s law is much more stronger than the magnitude of the gravitational force provided by Newton’s law of gravitation.
• The magnitude of the universal gravitational constant in Newton’s law of gravitation is very small, while the magnitude of the electrostatic force constant in Coulomb’s law is quite large.

Comparison between gravitational mass and electric charge

• The electric charge on an object can be positive or negative, whereas the gravitational mass of an object is a positive quantity. Due to this, the electric force between two charges can be attractive or repulsive, while the gravitational force always remains attractive.
• Electric charge always remains conserved, but mass is not conserved as it can be converted into energy.
• Electric charge always remains quantized, whereas the quantization of mass has not been established.