Electrostatic Force: Unraveling Its Mysteries and Applications

The electrostatic force is a fundamental force of nature that arises from the interaction between electrically charged particles. It is responsible for the attraction or repulsion between charged objects and plays a crucial role in various phenomena, such as static electricity and the behavior of atoms and molecules. The strength of the electrostatic force depends on the magnitude of the charges and the distance between them, following Coulomb’s law. It is an essential concept in the study of electromagnetism and has numerous applications in technology and everyday life.

Key Takeaways

Fact	Description
1.	The electrostatic force is a fundamental force that arises from the interaction between electrically charged particles.
2.	It is responsible for the attraction or repulsion between charged objects.
3.	The strength of the electrostatic force depends on the magnitude of the charges and the distance between them, following Coulomb’s law.
4.	The electrostatic force plays a crucial role in various phenomena, such as static electricity and the behavior of atoms and molecules.
5.	It is an essential concept in the study of electromagnetism and has numerous applications in technology and everyday life.

Understanding Electrostatic Force

Electrostatic force is a fundamental concept in physics that describes the interaction between electrically charged objects. It plays a crucial role in our understanding of how charged particles behave and interact with each other. In this section, we will explore the definition of electrostatic force, explain it in simple words, and delve into the equation and units associated with it.

Definition of Electrostatic Force

Electrostatic force, also known as Coulomb’s Law, is the force of attraction or repulsion between two electrically charged objects. It arises from the interaction of the electric fields created by these charges. The magnitude of the electrostatic force depends on the amount of charge on the objects and the distance between them.

When two objects have the same type of charge (both positive or both negative), they repel each other due to the electrostatic force. On the other hand, if the charges are of opposite types (one positive and one negative), they attract each other. This force of attraction or repulsion is responsible for many phenomena we encounter in our daily lives, such as the way a balloon sticks to a wall after being rubbed against our hair.

Electrostatic Force in Simple Words

To understand electrostatic force in simple words, imagine two magnets. When you bring the opposite poles of the magnets close to each other, they attract each other. This attraction is similar to the force between two objects with opposite charges. On the other hand, if you try to bring the same poles of the magnets together, you will feel a repulsive force pushing them apart. This repulsion is akin to the force between two objects with the same charges.

In essence, electrostatic force is like a “magnetic” force between electrically charged objects. It can either pull them together or push them apart, depending on the types of charges involved. This force is responsible for holding atoms and molecules together, as well as shaping the behavior of larger objects.

Electrostatic Force Equation and Units

The electrostatic force between two charged objects can be calculated using Coulomb’s Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

[F = frac{{k cdot |q_1 cdot q_2|}}{{r^2}}]

Where:
– F is the electrostatic force between the charges,
– k is the electrostatic constant (also known as the Coulomb constant),
– q1 and q2 are the magnitudes of the charges on the objects, and
– r is the distance between the charges.

The SI unit of charge is the Coulomb (C), and the SI unit of distance is the meter (m). Therefore, the SI unit of electrostatic force is the Newton (N).

It is important to note that the electrostatic force can be attractive (when the charges have opposite signs) or repulsive (when the charges have the same sign). The magnitude of the force depends on the amount of charge and the distance between the objects.

Nature of Electrostatic Force

The nature of electrostatic force is a fundamental concept in the study of electricity and magnetism. It describes the force that exists between electrically charged objects. This force can either be attractive or repulsive, depending on the types of charges involved.

Electrostatic Force as a Mutual Force

Electrostatic force is often referred to as a mutual force because it acts between two charged objects. According to Coulomb’s Law, the magnitude of the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This means that the force becomes stronger as the charges increase and weaker as the distance between them increases.

When two objects have opposite charges, such as a positive charge and a negative charge, they experience a force of attraction. On the other hand, when two objects have the same type of charge, such as two positive charges or two negative charges, they experience a force of repulsion. This mutual force is responsible for the interactions between charged particles and plays a crucial role in various phenomena, such as the behavior of magnets and the functioning of electronic devices.

Electrostatic Force as a Central Force

Another aspect of the nature of electrostatic force is that it acts as a central force. This means that the force always acts along the line joining the centers of the charged objects. The direction of the force depends on the types of charges involved. For opposite charges, the force is attractive and pulls the objects towards each other. For like charges, the force is repulsive and pushes the objects away from each other.

Electrostatic Force as a Field Force

Electrostatic force is also considered a field force. It means that the force is not limited to acting only between the charged objects but extends throughout the surrounding space. This force is mediated by the electric field, which is a region of influence created by electric charges. The electric field exerts a force on any other charged object placed within its influence.

The concept of electric field is crucial in understanding the nature of electrostatic force. It helps explain how the force between charged objects can be felt even without direct contact. The strength and direction of the electric field determine the magnitude and direction of the force experienced by a charged object.

Electrostatic Force as a Vector Quantity

Lastly, electrostatic force is a vector quantity. This means that it has both magnitude and direction. The magnitude of the force is determined by the charges and the distance between them, as described by Coulomb’s Law. The direction of the force is determined by the types of charges involved and follows the principle of action and reaction.

Characteristics of Electrostatic Force

Electrostatic force, also known as Coulomb’s Law, is a fundamental force in nature that governs the interaction between electrically charged objects. It is responsible for both the attractive and repulsive forces between charged particles. Let’s explore some of the key characteristics of electrostatic force.

Electrostatic Force and Distance Relationship

The electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This relationship is described by Coulomb’s Law. As the distance between the objects increases, the electrostatic force decreases, and vice versa. It is important to note that this relationship holds true for both positive and negative charges.

Electrostatic Force Dependence on Medium

The medium between charged objects can affect the strength of the electrostatic force. In general, the electrostatic force is stronger in a vacuum or air compared to other mediums. This is because the presence of other materials can influence the electric field and alter the force between charged objects. The permittivity of free space, also known as the electric constant, plays a role in determining the strength of the electrostatic force in different mediums.

Electrostatic Force Dependence on Mass

The mass of charged objects does not directly affect the electrostatic force between them. The force is solely determined by the charges and the distance between them. However, the mass of an object can indirectly influence the electrostatic force through its charge. For example, if two objects have the same charge but different masses, the force experienced by the lighter object will be greater due to its smaller inertia.

Electrostatic Force Dependence on Charge

The magnitude of the electrostatic force is directly proportional to the product of the charges on the objects. If the charges are of opposite signs (positive and negative), the force will be attractive, pulling the objects towards each other. On the other hand, if the charges are of the same sign (positive and positive or negative and negative), the force will be repulsive, pushing the objects away from each other. The greater the magnitude of the charges, the stronger the electrostatic force.

These characteristics of electrostatic force play a crucial role in various phenomena and applications, such as electric fields, electric potential, electric dipoles, electric flux, and electrostatic induction. Understanding the behavior of electrostatic force allows us to comprehend the behavior of charged objects and their interactions in electrostatic equilibrium. It also helps explain concepts like Gauss’s Law, conductors in electrostatic equilibrium, electric polarization, and electrostatic discharge.

Remember, electrostatic force is a fascinating aspect of nature that governs the behavior of electrically charged objects. Its understanding is essential in fields like physics, engineering, and everyday life, where static electricity and its effects are encountered.

Types of Electrostatic Force

Electrostatic force is a fundamental force in nature that arises from the interaction between electric charges. There are two main types of electrostatic force: the electrostatic force of attraction and the electrostatic force of repulsion.

Electrostatic Force of Attraction

The electrostatic force of attraction occurs when two objects with opposite electric charges are brought close together. According to Coulomb’s Law, this force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In other words, the greater the magnitude of the charges and the closer the objects are, the stronger the force of attraction.

This force plays a crucial role in various phenomena, such as the interaction between positive and negative charges in an atom, the binding of electrons to the nucleus, and the attraction between charged particles in chemical reactions. It is responsible for holding electrons in their orbits around the nucleus, creating stable atomic structures.

Electrostatic Force of Repulsion

On the other hand, the electrostatic force of repulsion occurs when two objects with the same electric charge are brought close together. Like the force of attraction, the force of repulsion follows Coulomb’s Law. However, in this case, the force is repulsive, pushing the objects away from each other.

This force is a result of the interaction between like charges, where the positive charges repel each other, as do the negative charges. It is this force that prevents objects from passing through each other and gives them a sense of solidity. Moreover, it is responsible for the repulsion between electrons in the outer shells of atoms, which determines the behavior of matter and the formation of chemical bonds.

To summarize, electrostatic force plays a crucial role in the behavior of electrically charged objects. It governs the interaction between positive and negative charges, leading to either attraction or repulsion. Understanding these forces is essential in various fields, including physics, chemistry, and electrical engineering.

Electrostatic Force of Attraction	Electrostatic Force of Repulsion
Opposite charges	Like charges
Attractive force	Repulsive force
Coulomb’s Law	Coulomb’s Law
Electric potential energy	Electric potential energy
Electric dipole	Electric dipole
Electric field	Electric field
Electric field lines	Electric field lines
Electric flux	Electric flux
Permittivity of free space	Permittivity of free space
Electrostatic equilibrium	Electrostatic equilibrium
Gauss’s Law	Gauss’s Law
Conductors in electrostatic equilibrium	Conductors in electrostatic equilibrium
Electric polarization	Electric polarization
Electrostatic induction	Electrostatic induction
Electric constant	Electric constant
Ionization	Ionization
Insulators and conductors	Insulators and conductors
Static electricity	Static electricity
Electric discharge	Electric discharge

Remember, electrostatic force is just one aspect of the fascinating world of electromagnetism. It is through the interplay of these forces that we can understand the behavior of charged particles and the intricate workings of the physical world around us.

Electrostatic Force in Physics and Chemistry

Electrostatic force is a fundamental concept in both physics and chemistry that describes the interaction between electrically charged objects. It is the force that exists between two charged particles, whether they are stationary or in motion. This force plays a crucial role in understanding the behavior of electrically charged objects and the principles that govern their interactions.

Electrostatic Force in Physics

In physics, the electrostatic force is governed by Coulomb’s Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law mathematically describes the strength of the electrostatic force and helps us understand how electric charges interact with each other.

When two objects have the same type of charge, either positive or negative, they experience a force of repulsion. This means that they push each other away due to the electrostatic force. On the other hand, when two objects have opposite charges, a force of attraction occurs. This force pulls the objects towards each other, as opposite charges attract each other.

Electrostatic Force of Attraction in Chemistry

In chemistry, the electrostatic force of attraction is particularly important when studying the behavior of atoms and molecules. Atoms consist of positively charged protons, negatively charged electrons, and neutral neutrons. The electrostatic force of attraction between the positively charged protons in the nucleus and the negatively charged electrons keeps the atom intact.

When atoms come together to form molecules, the electrostatic force of attraction plays a crucial role. It determines the stability and structure of molecules by holding the atoms together. For example, in an ionic bond, the electrostatic force of attraction between positively and negatively charged ions forms a strong bond.

Moreover, the concept of electric potential and electric dipole moment is also related to the electrostatic force. Electric potential refers to the electric potential energy per unit charge at a specific point in an electric field. Electric dipole refers to a pair of equal and opposite charges separated by a distance. The electrostatic force acts on the electric dipole, causing it to align with the electric field.

Understanding the electrostatic force in physics and chemistry is essential for comprehending the behavior of electrically charged objects and the principles that govern their interactions. From Coulomb’s Law to the force of attraction in chemistry, these concepts provide a foundation for further exploration of topics such as electric fields, electric potential energy, and electrostatic equilibrium. By studying the electrostatic force, we gain insights into the fundamental forces that shape our physical and chemical world.

Electrostatic Force vs Gravitational Force

Why Electric Force is Stronger than Gravitational

When comparing the electrostatic force and gravitational force, it becomes evident that the electric force is significantly stronger than the gravitational force. This difference in strength can be attributed to several factors.

Firstly, let’s consider Coulomb’s Law, which describes the relationship between electric charges and the force between them. According to this law, the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In contrast, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The electric charge of an object can be positive or negative, while the mass of an object is always positive. This means that the electric force can have both attractive and repulsive components, depending on the charges involved. On the other hand, the gravitational force is always attractive, pulling objects towards each other.

Furthermore, the electric force can act over much shorter distances compared to the gravitational force. The electric field, created by electric charges, diminishes rapidly with distance. In contrast, the gravitational field, created by masses, diminishes much more slowly. This means that the electric force can have a significant effect even at relatively small distances, while the gravitational force becomes weaker over larger distances.

Another important factor is the permittivity of free space, denoted by ε₀. This constant determines the strength of the electric force between charged objects. In comparison, the gravitational force does not have an equivalent constant, resulting in a weaker force overall.

Understanding How Electrostatic Forces Cancel

In certain situations, electrostatic forces can cancel each other out, resulting in a net force of zero. This phenomenon is known as electrostatic equilibrium. It occurs when the electric forces between charged objects balance each other perfectly.

One way electrostatic forces can cancel is through the formation of electric dipoles. An electric dipole consists of two equal and opposite charges separated by a small distance. The electric field lines originating from the positive charge and terminating at the negative charge cancel each other out, resulting in no net force.

Another mechanism for canceling electrostatic forces is through the process of electrostatic induction. This occurs when a charged object induces a separation of charges in a neutral object nearby. The induced charges create an electric field that cancels out the electric field of the charged object, leading to a net force of zero.

It is important to note that conductors in electrostatic equilibrium also exhibit the cancellation of electric forces. In conductors, charges redistribute themselves in such a way that the electric field inside the conductor is zero. This redistribution of charges ensures that the net force on the conductor is zero.

Understanding how electrostatic forces cancel is crucial in various fields, including electronics, where the behavior of electrically charged objects is of utmost importance. By comprehending the principles of electrostatic equilibrium, engineers and scientists can design and manipulate electrical systems effectively.

Practical Applications of Electrostatic Force

Electrostatic force, governed by Coulomb’s Law, plays a crucial role in various practical applications. From everyday life to advanced technologies, this force is utilized in numerous ways to achieve desired outcomes. Let’s explore some of the practical applications of electrostatic force.

How Electrostatic Force is Used in Everyday Life

1. Static Electricity: One of the most common examples of electrostatic force in everyday life is static electricity. When we rub certain materials together, such as a comb through our hair, electrons are transferred, resulting in an imbalance of electric charge. This imbalance creates a force of attraction or repulsion between objects, leading to phenomena like hair sticking to a comb or clothes clinging together after being in a dryer.

2. Air Purification: Electrostatic precipitators are widely used in industries and homes to remove pollutants from the air. These devices use electrostatic force to charge particles in the air, causing them to stick to oppositely charged plates or filters. This process effectively removes dust, smoke, and other harmful particles, improving air quality.

3. Photocopiers and Laser Printers: Electrostatic force is employed in photocopiers and laser printers to create images on paper. The process involves charging a photoconductive drum with a laser, which selectively discharges areas corresponding to the image. The charged toner particles are then attracted to the discharged areas, forming the desired image, which is then transferred and fused onto the paper.

4. Spray Painting: Electrostatic spray painting is widely used in industries and automotive applications. The paint particles are given an electric charge as they leave the spray gun, while the object being painted is grounded. The charged particles are attracted to the grounded object, resulting in a more even and efficient coating process.

Examples of Electrostatic Force

Here are a few more examples of how electrostatic force is applied in various fields:

Application	Description
Electrostatic Precipitators	Used in power plants to remove ash and other particulate matter from flue gases.
Inkjet Printing	Utilizes electrostatic force to control the movement of ink droplets onto paper, creating high-resolution images.
Electrostatic Motors	These motors use the repulsion and attraction between electric charges to generate rotational motion.
Electrostatic Discharge (ESD) Protection	In electronic devices, components like diodes and capacitors are used to protect against sudden electrostatic discharges that could damage sensitive circuits.
Electrostatic Force Microscopy (EFM)	A technique used in nanotechnology to study the electrical properties and surface topography of materials at the atomic level.

These examples demonstrate the wide-ranging applications of electrostatic force in our daily lives and various industries. Understanding and harnessing this force has led to significant advancements in technology, improving our quality of life and enabling innovative solutions in diverse fields.

Calculating Electrostatic Force

Electrostatic force is a fundamental concept in physics that describes the interaction between electrically charged objects. It is the force that exists between two charged particles, whether they are positive or negative. Understanding how to calculate electrostatic force is crucial in various fields, including electromagnetism, electronics, and even everyday life.

Electrostatic Force Formula

The electrostatic force between two charges can be calculated using Coulomb’s Law. This law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F = k * (q1 * q2) / r^2

Where:
– F is the electrostatic force between the charges,
– k is the electrostatic constant or the permittivity of free space,
– q1 and q2 are the magnitudes of the charges, and
– r is the distance between the charges.

Electrostatic Force Between Two Charges

When two charges have the same sign (both positive or both negative), the electrostatic force between them is one of repulsion. This means that they will push each other away. On the other hand, when two charges have opposite signs (one positive and one negative), the electrostatic force between them is one of attraction. They will be pulled towards each other.

The magnitude of the electrostatic force between two charges is directly proportional to the product of their magnitudes. If the charges are doubled, the force will also double. Similarly, if the distance between the charges is halved, the force will quadruple.

How to Calculate Electrostatic Force

To calculate the electrostatic force between two charges, follow these steps:

1. Determine the magnitudes of the charges (q1 and q2) in Coulombs.
2. Measure the distance (r) between the charges in meters.
3. Find the value of the electrostatic constant (k), which is approximately equal to 9 × 10^9 Nm^2/C^2.
4. Plug the values into the electrostatic force formula: F = k * (q1 * q2) / r^2.
5. Calculate the force using the formula and express it in Newtons (N).

It is important to note that the direction of the electrostatic force depends on the charges involved. The force of attraction will be towards each other for opposite charges, while the force of repulsion will be away from each other for like charges.

Understanding how to calculate electrostatic force is essential in various applications, such as designing electrical circuits, analyzing the behavior of charged particles, and predicting the behavior of electrically charged objects. It allows us to comprehend the forces at play and make informed decisions in various scientific and technological endeavors.

Remember, electrostatic force is just one aspect of the fascinating world of static electricity, which encompasses concepts like electric fields, electric potential, electric dipole, electric flux, and more. Exploring these concepts further can deepen our understanding of the behavior of charged objects and their interactions in different scenarios.

Interesting Facts about Electrostatic Force

Discovery of Electrostatic Force

One of the most fascinating facts about electrostatic force is its discovery by Charles-Augustin de Coulomb in the late 18th century. Coulomb’s Law, named after him, describes the relationship between electric charges and the force they exert on each other. This law paved the way for our understanding of the fundamental principles of electrostatics.

Can Electrostatic Force be Negative?

Electrostatic force can indeed be negative. This occurs when two charged objects have opposite charges. For example, if a positively charged object and a negatively charged object are brought close together, they will experience an attractive force. The negative sign indicates the direction of the force, which is towards each other.

Is Electrostatic Force Always Attractive?

No, electrostatic force is not always attractive. It can also be repulsive. When two objects with the same type of charge, either positive or negative, are brought close together, they will experience a force of repulsion. This means that the force pushes the objects away from each other. It is important to note that the magnitude of the force remains the same, but the direction is opposite for attractive and repulsive forces.

To better understand the concepts related to electrostatic force, let’s take a look at some key terms and phenomena:

• Electric Charge: Electric charge is a fundamental property of matter that can be positive or negative. It is the source of electrostatic force.

• Electric Field: The electric field is a region around a charged object where the electric force can be felt. It is created by electric charges and can exert a force on other charged objects.

• Electric Potential: Electric potential refers to the amount of electric potential energy per unit charge at a specific point in an electric field. It is a measure of the work done to move a unit positive charge from infinity to that point.

• Electric Dipole: An electric dipole consists of two equal and opposite charges separated by a small distance. It is a common configuration in many electrostatic systems.

• Electric Flux: Electric flux is a measure of the electric field passing through a given area. It is proportional to the number of electric field lines passing through the area.

• Permittivity of Free Space: Permittivity of free space, denoted by ε₀, is a physical constant that relates the electric field to the electric charge in a vacuum.

• Electrostatic Equilibrium: Electrostatic equilibrium refers to a state where the electric field inside a conductor is zero. In this state, the charges are distributed in such a way that there is no net movement of charge.

• Electric Field Lines: Electric field lines are imaginary lines used to represent the direction and strength of the electric field. They always point away from positive charges and towards negative charges.

• Electrostatic Induction: Electrostatic induction is the process of redistributing the electric charge on an object by bringing it close to a charged object without direct contact. This phenomenon is the basis for many practical applications.

• Electrostatic Potential Energy: Electrostatic potential energy is the potential energy associated with the configuration of charged objects in an electric field. It depends on the relative positions and magnitudes of the charges.

• Gauss’s Law: Gauss’s Law is a fundamental principle in electrostatics that relates the electric flux through a closed surface to the total charge enclosed by that surface.

• Conductors in Electrostatic Equilibrium: In electrostatic equilibrium, charges on conductors reside on their outer surfaces. This is due to the repulsion between like charges, which causes them to distribute themselves as far apart as possible.

• Electric Polarization: Electric polarization refers to the process of separating positive and negative charges within an insulating material when it is subjected to an external electric field.

• Electrostatic Discharge: Electrostatic discharge is the sudden flow of electric charge between two objects with different electric potentials. It occurs when there is a buildup of static electricity and can result in a visible spark or a mild shock.

• Electric Constant: The electric constant, denoted by ε, is a physical constant that relates the electric field to the electric charge in a medium other than a vacuum.

• Ionization: Ionization is the process of converting an atom or molecule into ions by adding or removing electrons. It plays a crucial role in the generation and behavior of electrically charged objects.

• Insulators and Conductors: Insulators are materials that do not allow the easy flow of electric charge, while conductors are materials that allow the free movement of electric charge. The behavior of electrostatic force differs between these two types of materials.

These interesting facts and concepts shed light on the intriguing nature of electrostatic force and its role in our everyday lives. From the discovery of Coulomb’s Law to the various phenomena associated with electric charges, electrostatics continues to captivate scientists and engineers alike.

Frequently Asked Questions

1. What is Electrostatic Force?

Electrostatic force is the physical force that electrically charged particles exert on each other. It can be attractive or repulsive depending on the nature of the charges involved. This force is described by Coulomb’s Law.

2. What is the Electrostatic Force Formula?

The formula for electrostatic force is derived from Coulomb’s Law and is given as F = k * |q1*q2| / r^2, where F is the force, k is Coulomb’s constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

3. Why is Electrostatic Force Considered a Central Force?

Electrostatic force is considered a central force because it always acts along the line joining the centers of two charges, irrespective of their position. This is a characteristic of central forces.

4. Does Electrostatic Force Depend on the Medium?

Yes, the electrostatic force between two charges can depend on the medium in which they are placed. This is because the permittivity of the medium affects the force. In vacuum or air, the force is maximum, while in other media, it is less than that in vacuum.

5. Is Electrostatic Force a Field Force?

Yes, electrostatic force is a field force. It is the force experienced by a charge in an electric field created by another charge. It doesn’t require physical contact between the charges, hence it’s a field force.

6. How Does Electrostatic Force Depend on Charge?

The electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This relationship is stated in Coulomb’s Law.

7. Can Electrostatic Force be Negative?

Yes, electrostatic force can be negative. A negative force indicates that the force is attractive. This happens when one charge is positive and the other is negative.

8. Is Electrostatic Force a Vector Quantity?

Yes, electrostatic force is a vector quantity. It has both magnitude (the strength of the force) and direction (the line along which the force acts).

9. How is Electrostatic Force Used in Everyday Life?

Electrostatic force is used in everyday life in many ways. For example, it’s the force that causes static electricity, which can make your hair stand on end or cause a spark when you touch a metal object. It’s also used in photocopiers and laser printers to transfer toner to the paper.

10. Why is Electric Force Stronger Than Gravitational Force?

Electric force is stronger than gravitational force because the electromagnetic constant is much larger than the gravitational constant. For example, the electrostatic force between an electron and a proton is about 10^36 times stronger than the gravitational force between them.