How to compare Electric Force and Gravity with similarities and differences?

This topic is a comparative study between the Electric force and Gravity. The electric force is related to electric charges and Gravity is applicable between any two masses.

Similarities between the laws explaining Electric Force and Gravity

Coulomb’s law for the force between two charges looks pretty similar to Newton’s law of gravitation for the force between two masses.

Both the laws are inverse-square laws, meaning the force diminishes with the square of the distance.

The product of the two charges in Coulomb’s law resembles the product of the masses in Newton’s law.

Differences between the Electric Force and Gravity

There are a couple of important differences.

1 ) One is that the electric force can be attractive or repulsive, depending on the signs of the charges, but the force of gravity is always attractive.

2 ) Another important difference is the strength of the forces of gravity and electricity.

We can compare the two forces is in a hydrogen atom,
where a proton and electron attract each other electrically and gravitationally.

Here we will use the average distance between the proton and the electron = r = 5.3 × 10-11 m.

Now, using Newton’s Law of Gravitation, we get 3.6 × 10-47 N for gravity. As we use Coulomb’s law, we received 8.2 × 10-8 N for the electric force between the proton and electron.

That’s a huge difference. The electric force is a clear winner with almost 1039 times magnitude than its competitor!

Electric Force is much stronger than the Gravity

The electric force is a clear winner with almost 1039 times magnitude than the gravity when we calculated those between the electron and proton in a hydrogen atom.

This clearly explains why electric forces dominate over gravity even when we have a fairly slight excess of charge, such as when we’ve run a comb through our hair.

The big difference in the strength of the two forces also tells us that whenever gravity is the dominant force, the bodies involved are extremely neutral electrically. For example, Earth’s orbit around the sun is accounted for by Newton’s law of gravitation. That tells us that the net charge on Earth is pretty small.

How to compare Electric Force and Gravity with similarities and differences?
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