Similarities and dissimilarities between Coulomb's force and gravitational force

Here we discussed the 5 points on the similarities and dissimilarities between Coulomb’s force (or electrostatic force) and gravitational force. But before we proceed to the similarities and differences we should know the definitions of coulomb’s force and gravitational force respectively.

What is coulomb’s force?

Coulomb’s force is an electrostatic force of repulsion or attraction between two stationary charged bodies that is directly proportional to the product of the charge. But inversely proportional to the square of the distance between them.

F ∝ q¹ q² / r²

credit – shutterstock.com

The formula of coulomb’s force is given as:

F = k q¹×q² / r²

Notable points about coulomb’s force.

Coulomb’s force depends on the magnitude of the charged bodies.
It is an electrostatic force.
S.I unit of coulomb’s force is Newton.
Coulomb’s force is valid for stationary bodies.
Coulomb’s force is vector quantity.
Value of coulomb’s force can be negative, positive or zero.
Coulomb’s force can be possible for at least two different charged bodies.

What is gravitational force?

Gravitational force is also an attractive or repulsive force that is directly proportional to the product of the masses of the body. But inversely proportional to the square of the distance between them.

credit – shutterstock

Notable points on gravitational force

Gravitational force depends on the magnitude of the uncharged bodies.
It is not an electrostatic force.
S.I unit of gravitational force is Newton.
Gravitational force is valid for moving or stationary bodies.
Gravitational force is vector quantity.
Value of gravitational force can be negative, positive or zero.
Gravitational force also can be possible for at least two different bodies.

Please note that we use electrostatic forces in place of coulomb’s forces in some places. Because both the forces have same meaning.

Similarities between coulomb’s force and gravitational force

Both Forces Coulomb’s and gravitational are directly proportional to the product of charges and masses of the body.
Both Forces coulomb’s and gravitational are inversely proportional to the square of distance between them.
Both forces are central forces.
Both forces are conservative forces.
Both forces can be calculated even in vaccum.

Here is the top 5 plus dissimilarities or differences between electrostatic (or coulomb’s force) and gravitational forces.

Coulomb’s force and gravitational force are both fundamental forces in nature that govern the interactions between objects. However, they differ in several key aspects. Below is a comparison that highlights their similarities and differences:

More similarities Between Coulomb’s Force and Gravitational Force

Inverse Square Law:
Both forces obey the inverse square law, meaning the magnitude of the force decreases with the square of the distance between the two interacting objects.
- Coulomb’s Force: $F = frac{k_e |q_1 q_2|}{r^2}$
- Gravitational Force: $F = frac{G |m_1 m_2|}{r^2}$
  Where:
- $q_1, q_2$ are the charges,
- $m_1, m_2$ are the masses,
- $r$ is the distance between the objects,
- $k_e$ and $G$ are constants (Coulomb’s constant and the gravitational constant, respectively).
Action-at-a-Distance:
Both forces are long-range forces and act over a distance without requiring physical contact between the objects. They both affect objects even if they are not in direct contact.
Central Forces:
Both forces are central forces, meaning they act along the line connecting the centers of the two interacting objects.
Conservative Forces:
Both are conservative forces, meaning that the work done by these forces depends only on the initial and final positions, and not on the path taken.
Force is Directly Proportional to the Magnitudes:
In both cases, the force is proportional to the product of the interacting quantities:

For Coulomb’s force, the force is proportional to the product of the charges ( $q_1 times q_2$ ).
For gravitational force, the force is proportional to the product of the masses ( $m_1 times m_2$ ).

Differences between electrostatic force and gravitational force

Electrostatic force can be the force of attraction or repulsion between two charges at rest, while gravitational force is the force of only attraction between two bodies.
Coulomb’s force can attract or repel the objects but gravitational force can only attract the bodies not can repel.
Electrostatic force (or coulomb force) depends on the nature of the medium while gravitational force doesn’t depends on the medium even it can be applicable in outer space.
The value of electrostatic force changes as medium change but the value of gravitational force doesn’t changes as medium change.
Electrostatic force has highly greater value than gravitational forces.
Electrostatic force is very strong force while gravitational force is weak force as compared to coulomb force.

More dissimilarities Between Coulomb’s Force and Gravitational Force

Property	Coulomb’s Force	Gravitational Force
Nature of Interaction	Acts between electric charges (positive or negative).	Acts between masses (always attractive).
Attraction or Repulsion	Attractive or Repulsive: Depending on the charges’ sign (like charges repel, opposite charges attract).	Always Attractive: Gravitational force always attracts masses towards each other.
Strength	Very Strong: Coulomb’s force is much stronger than gravity at the atomic and molecular levels.	Very Weak: Gravitational force is extremely weak compared to electromagnetic forces, especially at small scales.
Sign of the Force Constant	The force constant, $k_e$ , is positive, indicating both attraction and repulsion.	The force constant, $G$ , is positive, but the force is always attractive.
Range of Effect	Long-range, but can be neutralized if equal positive and negative charges are present.	Long-range but never neutralized (always acts, no cancellation).
Dependence on Medium	Coulomb’s force depends on the medium in which charges are placed. The force is reduced in a dielectric medium.	Gravitational force is independent of the medium and only depends on mass and distance.
Force Constant	Coulomb’s constant $k_e$ is much larger than the gravitational constant $G$ (i.e., $k_e approx 8.99 times 10^9 , text{N·m}^2/text{C}^2$ , $G approx 6.67 times 10^{-11} , text{N·m}^2/text{kg}^2$ ).	Gravitational constant $G$ is very small, which makes gravitational forces relatively weak compared to electrostatic forces.
Origin	Coulomb’s force originates from electric charges and is described by electromagnetic interaction.	Gravitational force originates from mass and is described by gravitational interaction.
Relative Magnitude	The electromagnetic force is significantly stronger than the gravitational force, especially at atomic and molecular scales.	The gravitational force is incredibly weak compared to electromagnetic force, especially at small scales.
Effect at Small Scales	At atomic or molecular scales, Coulomb’s force dominates the behavior of particles (e.g., electrons and protons).	At atomic or molecular scales, gravitational force is negligible compared to Coulomb’s force and does not influence particle behavior.
Mathematical Expression	( F = frac{k_e	q_1 q_2

Key Takeaways:

Coulomb’s force is stronger and can be both attractive and repulsive, acting between electric charges.
Gravitational force is always attractive and acts between masses, but it is much weaker than Coulomb’s force.
Gravitational force is significant on large scales (like celestial bodies), while Coulomb’s force dominates at small, atomic, and molecular scales.

Similarities and dissimilarities between Coulomb’s force and gravitational force