Question

what causes electrical charges to attract and repel? how does the strength of this force compare to the gravitational force?

Answer 1

1) The electromagnetic force

2) The electric force is approximately $1.3\cdot 10^{20}$ times stronger than the gravitational force.

Explanation:

1)

There are four fundamental forces in nature:

• The gravitational force, acting between objects having mass
• The electromagnetic force, acting between objects having electric charge
• The strong nuclear force, holding protons and neutrons together in the nuclei of the atoms
• The weak nuclear force, responsible for certain types of radioactive decay

Here we are interested in the electromagnetic force, which is the force that causes electric charges to attract or repel. In fact, two electric charges feel a mutual force (the electromagnetic force), whose nature is:

• Attractive, if the charges have opposite  signs
• Repulsive, if the charges have same sign

The magnitude of this force is given by Coulomb's law:

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

where

k is the Coulomb's constant

q1, q2 are the two charges

r is the separation between the two charges

2)

In order to compare the  strength of the electric force to that of the gravitational force, we have to take two sample objects of mass 1 kg (unit mass) and of charge 1 C (unit charge), place them at 1 metre distance, and compute the value of both forces.

The gravitational force is given by:

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

where

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

$m_1 = m_2 = 1 kg$ are the masses of the two objects

r = 1 m is the separation between them

The electric force is given by:

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

where:

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

$q_1 = q_2 = 1 C$ are the two charges

r = 1 m is the separation between the two charges

Calculating the ratio between the two forces, we  find

$\frac{F_E}{F_G}=\frac{k}{G}=\frac{8.99\cdot 10^9}{6.67\cdot 10^{-11}}=1.3\cdot 10^{20}$

From which we see that the electric force is approximately $1.3\cdot 10^{20}$ times stronger than the gravitational force.

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