Question

How is Coulomb’s law similar to newton’s law of gravitational force? How is it different

Answer 1

The similarities and the differences between gravitational and electric force are listed below

Explanation:

- The magnitude of the gravitational force between two objects is given by Newton's law of gravitation:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

$m_1, m_2$ are the masses of the two objects

r is the separation between them

- Coloumb's law gives instead the strength of the electrostatic force between two charged objects, which is

$F=k\frac{q_1 q_2}{r^2}$

where:

$k=8.99\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1, q_2$ are the two charges

r is the separation between the two charges

By comparing the two equations, we find the following similarities:

• Both the forces are inversely proportional to the square of the distance between the two objects, $F\propto \frac{1}{r^2}$
• Both the forces are proportional to the product between the "main quantity" of each force, which is the mass for the gravitational force ($F\propto m_1 m_2$) and the charge for the electric force ($F\propto q_1 q_2$

Instead, we have the following differences:

• The gravitational force is always attractive, since the sign of $m$ is always positive, while the electric force can be either attractive or repulsive, since the sign of $q$ can be either positive or negative
• The value of the gravitational costant G is much smaller than the value of the Coulomb's constant, so the gravitational force is much weaker than the electric force

Learn more about gravitational force and electric force:

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