Gravitational and Electric Forces

Four fundamental interactions are constantly happening all around us at every moment, all across the universe. In this article, well explore definitions and examples of two of the four fundamental forces: the gravitational force and the electric force.

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    What Are Gravitational and Electric Forces?

    The two most familiar interactions that run the universe as we know it are the gravitational force and electrical force.

    The gravitational and electric forces are two of the four basic physical interactions that masses in the universe experience. These forces influence the motion, behavior, and structure of particles at different scales.

    Knowing why both are so foundational will build your understanding of many other topics in physics — lets dive into the details of these 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. Its also the weakest force.

    The gravitational force is the classical explanation for the attraction of all masses to one another in the universe across infinite ranges of distance.

    The gravitational interaction is always attractive, pulling masses together. Why? Gravity doesnt 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.

    A gravitational field is a vector field around a mass that describes what the magnitude and direction of gravitation would be if we were to place a very small mass somewhere in that field.

    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

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

    Fg=Gm1m2r2,

    wherem1andm2are the masses of two objects,ris the distance between the two masses, andGis the universal gravitational constant,G=6.674·10-11 m3kg s2. The gravitational constant is a constant of proportionality for all gravitational forces and fields in the universe.

    In your studies, you might also see the variable d used instead of r. Both refer to distance, but r makes it clear that were measuring the distance from the centers of two point-like (or approximated point) sources of mass.

    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!

    Gravitational and Electric Forces Two masses of different sizes gravitationally attract with a force equal in magnitude StudySmarter

    The universal attraction of all masses means two objects of any size will attract each other with a force equal in magnitude, Wikimedia Commons CC BY-SA 4.0

    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.

    Classical gravity theories have been around as an explanation for the acceleration of objects on Earth for hundreds of years. Galileo, Newton, Huygens, and other scientists questioned the reason objects accelerated toward the ground after being dropped, and imagined a force that causes this behavior. The work of Einstein meant that gravity might not be a force. Instead, the theory of general relativity explains that mass bends spacetime itself. And even more recently, researchers are actively searching for a particle that can explain gravity at a quantum level.

    Why should we still care about the classical gravity theory, then? Newer theories don’t mean that the description of gravity as an attractive force is completely inaccurate. Modern theories are especially useful when talking about supermassive objects like black holes or objects traveling at high speed, but Newton’s original law of universal gravitation is still a useful tool for explaining gravitational attraction on Earth and within our Solar System. Though general relativity is beyond AP Physics 1, it’s useful to know of the different theories we use to explain our universe!

    The Electric Force Definition

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

    The electric or electrostatic force is the interaction between charged particles, such as electrons and protons at rest, whereby they may be attracted to or repelled by each other.

    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 were 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.

    An electric field is a vector field that describes what the magnitude and direction of an electric force would be if we were to place a charge somewhere in that field.

    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.

    Gravitational and Electric Forces Field lines between a positive and negative charge attracting one another StudySmarterField lines between a positive and negative point charge, Wikimedia Commons CC BY-SA 3.0

    What do we mean by “only electric forces at rest” here? When we add charges in motion to the picture, we introduce magnetic fields and forces, too. Magnetism results from moving charges, so electricity and magnetism are often discussed together as a single concept. If youre curious to learn more now, see the Fundamental Forces article or learn more in AP Physics 2!

    Lets look at the law and equation behind the electric force next.

    The Electric Force Equation

    The electric force equation is commonly known as Coulombs Law. This equation is written as:

    FE=kq1q2r2,

    wherekis the Coulomb constant with a value ofk=8.987·109 N m2C2,q1andq2are the quantities and signs of two charges, andris the distance between the two charges. Thoseqcharges are measured in Coulombs, a unit of electric charge. Coulombs Law will give us a final answer in units of newtons.

    A coulomb is a unit of electric charge derived from current and time represented by the symbolC.

    1 Coloumb = 1 Ampere · 1 second

    Lets look at Coulombs 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.

    Gravitational and Electric Forces Repelling force of two positive charges and attractive force of two different charges StudySmarterThe electric force between two charged particles at a distance r apart can be calculated with Coulombs 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 lets go through a real-world example.

    Have you ever reached to open a door, and experienced a quick zap from static electricity upon touching the doorknob? This phenomenon happens if youve picked up some extra electrons. Maybe you shuffled your feet across a carpeted room, or your clothes are fresh out of the dryer machine. Rubbing these insulating materials together causes your body to pick up a charge, and touching that metal doorknob discharges the extra charge you accumulated!

    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.
    • Its also called the electrostatic force when charges are at rest. Coulombs 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.

    Youll 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. Its 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 youve been paying close attention to the characteristics of both the gravitational and electric forces, you might have noticed some similarities between these laws! Heres a handy table of both the similarities and differences youll want to remember between the two.

    Quality

    Gravitational, electric, or both?

    A fundamental force of physics

    Both

    Obeys an inverse-square law for distance

    Both

    Acts over infinite distance ranges

    Both

    Attractive force

    Both

    Repulsive force

    Electric

    Depends on charge

    Electric

    Dominates over short ranges

    Electric

    Forces or fields can be canceled out

    Electric

    Depends on mass

    Gravitational

    Dominates over very long ranges

    Gravitational

    Gravitational Force and Electric Force Examples

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

    A satellite orbiting Earth at a distance ofr=4.20·104 kmfrom the planets center has a mass of2.35·103 kg. Using the valuem=5.97·1024 kgfor the mass of the Earth, find the gravitational force exerted between the satellite and the Earth.

    This question calls for Newtons law of universal gravitation. Lets plug in our values — and dont forget, we need to change kilometers to meters!

    Fg=Gm1m2r2Fg=6.67·10-11 m3kg s2·(5.97·1024 kg)(2.35·103 kg)(4.20·107 m)2Fg=5.31 ·102 N

    The gravitational force between these two bodies is531 N.

    Now that youve seen the gravitational force equation in action, lets do an example using the electric force equation.

    Say we have two charges located18.0 cmapart. Charge 1 has a value of24.0 μC(micro-coulombs), and charge 2 has a value of-11.0 μC. What is the electric force charge 1 exerts on charge 2? Is the force attractive or repulsive?

    Plug the known values into the electric force equation and solve. Remember to convert micro-coulombs to coulombs, and centimeters to meters!

    FE=kq1q2r2FE=8.99·109 N m2C2·(2.40·10-5 C)(-1.10·10-5 C)(0.180 m)2FE=-73.3 N

    The sign of the final answer is negative, meaning the force exerted is attractive, pulling the two charges together.

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

    Gravitational and Electric Forces - Key takeaways

    • Gravitational and electric forces are both fundamental forces of physics, both of which drive much of the physical structure and behavior in our universe.
    • The gravitational force attracts all masses to one another.
    • The electric force can be either attractive or repulsive between two charges, where like charges repel and opposite charges attract.
    • Both the gravitational and electric forces operate at infinite distance, but both fall off in strength with increased distance due to the inverse-square distance laws.
    Frequently Asked Questions about Gravitational and Electric Forces

    What is true for both gravitational and electric forces?

    Both gravitational and electric forces have an infinite range of distance to act. Both gravitational and electric forces have a distance dependence of 1/d^2, so the strengths of the forces weaken with greater distances.

    What are gravitational and electric forces?

    Gravitational and electric forces are two forces of nature that influence the motion and structure of mass in the universe. The gravitational force is the universal attraction of all masses to one another. The electric force is the interaction of charges and charged matter at rest.

    Do gravitational and electric forces have infinite reach?

    Gravitational and electric forces have infinite reach. The gravitational and electric fields from a source of mass have an infinite range. The strength of both forces is proportional to the squared inverse distance, so both gravitational and electric forces will become weak with increased distances between two masses.

    How are gravitational forces and electric forces different?

    Gravitational forces and electric forces are different in that the gravitational force is always attractive, but the electric force can be either attractive or repulsive. Electric fields can be canceled due to the existence of positive and negative charges, but gravity cannot be canceled out. The gravitational force acts at long ranges while the electric force acts over a short distance.

    Which is stronger, the gravitational force or electric force?

    The electric force is stronger than the gravitational force by a factor of roughly 10e40. The gravitational force is the weakest of the fundamental forces of nature.

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    Test your knowledge with multiple choice flashcards

    What type of law does the distance for gravitational and electric forces obey?

    What is the SI unit for charge?

    True or false: the gravitational force can be both attractive and repulsive.

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