Gravitational and Electric Forces

The Gravitational Force Definition

The gravitational force is likely the force you know best: it keeps all the objects on the surface of the Earth grounded, accelerates the phone you dropped to the floor, and holds all of the orbiting bodies in our Solar System together. It’s also the weakest force.

The gravitational interaction is always attractive, pulling masses together. Why? Gravity doesn’t have a positive or negative component like the charges of protons, electrons, and other particles do. Because mass itself is always positive, the gravitational force always attracts. If mass could have a negative value, we would see gravitational fields that repel other masses, but a universe with these laws might not be one we could survive in!

You’ve likely heard the term “gravitational field” in the past, and wondered how that differs from the definition of the gravitational force. Gravitational fields are another term you’ll encounter throughout your studies of the fundamental forces.

Now that we’ve brushed up on our understanding of the gravitational force, let’s dive into the famous equation driving this fundamental interaction.

The Gravitational Force Equation

Newton’s law of universal gravitation, the equation for the gravitational force exerted between two objects with mass, is written as:

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

where$m_1$and$m_2$are the masses of two objects,$r$is the distance between the two masses, and$G$is the universal gravitational constant,$G=6.674·{10}^{-11}\frac{{\mathrm{m}}^3}{\mathrm{kg}{\mathrm{s}}^2}$. The gravitational constant is a constant of proportionality for all gravitational forces and fields in the universe.

The gravitational force is equal in magnitude for both objects — both objects are gravitationally attracting one another. Using the mass of the Earth and the mass of your own body as an example, the force you exert on the planet is equal to the force the planet exerts on you!

When a gravitational force is exerted on an object, the energy and work are conserved, meaning energy cannot be created or destroyed due to gravity. If a phone is dropped off the roof of a building, the force of gravity accelerates the phone downward, and potential energy is converted into kinetic energy.

Understanding the Gravitational Force

We know that gravitational attraction is a property of all mass. What else is there to know? One thing you might be curious about is the difference between the classical theory of gravity and modern theories.

The Electric Force Definition

The electric force, also called the electrostatic force for systems at rest, is a force between two charges.

Electric charges are a physical property of particles. Atoms, which are composed of electrons, protons, and neutrons, can be negatively or positively charged if the electrons and protons are not balanced.

These interactions between charged particles are usually too tiny for us to observe with our eyes alone, but many physical phenomena we’re familiar with on a macroscopic scale are thanks to these forces operating at atomic and subatomic scales. At atomic and subatomic scales, the electric force dominates over the gravitational force, meaning that the force of gravity between particles can be ignored.

Just like the gravitational force, electric forces have a field component as well. Indeed, charged particles have an electric field surrounding them.

Electric fields can look a lot of different ways. Most importantly, you should remember that unlike the gravitational force, electric interactions can be attractive or repulsive, depending on the signs of the charges involved. Let’s take a look at an example of the field lines between a single positive and single negative charge.

Field lines between a positive and negative point charge, Wikimedia Commons CC BY-SA 3.0

Let’s look at the law and equation behind the electric force next.

The Electric Force Equation

The electric force equation is commonly known as Coulomb’s Law. This equation is written as:

$F_{\mathrm{E}}=k\frac{q_1{q}_2}{r^2}$,

where$k$is the Coulomb constant with a value of$k=8.987·{10}^9\frac{\mathrm{N}{\mathrm{m}}^2}{{\mathrm{C}}^2}$,$q_1$and$q_2$are the quantities and signs of two charges, and$r$is the distance between the two charges. Those$q$charges are measured in Coulombs, a unit of electric charge. Coulomb’s Law will give us a final answer in units of newtons.

Let’s look at Coulomb’s Law for two identical charges and two different charges in the next figure. Here we can see that two positive charges (or two negative charges) will push each other away, while a positive and a negative charge will attract.

The electric force between two charged particles at a distance r apart can be calculated with Coulomb’s Law, Wikimedia Commons CC BY-3.0

If we just want the magnitude of the electric force, we can take the absolute value of the product of the two charges, as seen in the previous figure. This is useful if we want to know how strong the force exerted between two charges is without caring about the direction.

Key Characteristics of the Electric Force and Gravitational Force

We learned that just like the gravitational force, the electric force between two particles is attractive — however, this is only true for two particles with opposite charges. Here we see a divergence in similarities to the force of gravity. When two charges are the same, the electric force will repel instead.

You might be wondering what the electric force looks like in action, so let’s go through a real-world example.

To summarize so far, here are the most important characteristics to remember about the electric force.

• The electric force acts between charged particles at atomic and subatomic scales.
• It’s also called the electrostatic force when charges are at rest. Coulomb’s Law is the physical law and equation of the electrostatic force.
• It dominates over the gravitational force at tiny scales, the size of an atom or smaller.
• The electric force is attractive if two charges are different and repulsive if two charges are the same.
• The electrostatic force is directly proportional to the product of the two charges, and inversely proportional to the distance between the two charges.

You’ll learn more about electric and magnetic forces in AP Physics 2 — for now, the most important point to keep in mind moving forward is that the force exerted between two charges is equal in magnitude, and the strength of the force is inversely proportional to the squared distance.

Before moving on to comparing these two fundamental interactions, let’s summarize what we learned about gravity. Remember these key characteristics of the gravitational force.

• The gravitational force is the weakest of the four fundamental forces.
• Gravitation is always attractive and acts on the centers of objects or the center of mass between multiple objects.
• The force of gravity is inversely related to the squared distance between two objects. It’s also directly related to the total mass of two objects.
• Total energy and work due to the force of gravity are conserved — potential energy from the height of an object is converted to kinetic energy.
• Gravity acts over long distances, considerably longer than the scale of the electric force.

Comparisons of the Gravitational and Electric Forces

If you’ve been paying close attention to the characteristics of both the gravitational and electric forces, you might have noticed some similarities between these laws! Here’s a handy table of both the similarities and differences you’ll want to remember between the two.

Gravitational Force and Electric Force Examples

Let’s go through an example to see what using the gravitational force equation looks like in a physics problem.

Now that you’ve seen the gravitational force equation in action, let’s do an example using the electric force equation.

These laws feel pretty similar to one another in physics problems like the two previous examples. As you learn more about the fundamental forces, you’ll encounter problems solving for different unknown values.