Chapter 7: Problem 7

In otherwise empty space, what would happen if the size of the clectrostatic force acting between two positively charged objects was exactly the same as that of the gravitational force acting between them? What would happen if they were moved closer together or farther apart?

Short Answer

Expert verified

Answer: When the electrostatic force and gravitational force between two positively charged objects are equal, the objects would neither attract nor repel each other. However, when the distance between the objects changes, the electrostatic force will dominate. As the objects move closer together, they will repel each other more strongly due to the increased electrostatic force, whereas when moved farther apart, they will continue to repel each other, but less strongly.

Step by step solution

Identify the formulas for electrostatic and gravitational forces

The formula for the electrostatic force between two charged objects is given by Coulomb's law: F_e = k * |q1 * q2| / r^2 where F_e is the electrostatic force, k is Coulomb's constant (8.99 * 10^9 N * m^2 / C^2), q1 and q2 are the charges on the two objects, and r is the distance between them The formula for the gravitational force between two objects is given by Newton's law of gravitation: F_g = G * m1 * m2 / r^2 where F_g is the gravitational force, G is the gravitational constant (6.674 * 10^(-11) N * m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.

Set electrostatic force equal to gravitational force

To find the condition when the electrostatic force is equal to the gravitational force, we can set F_e equal to F_g: k * |q1 * q2| / r^2 = G * m1 * m2 / r^2

Analyze the change of forces when the distance changes

When two positively charged objects are moved closer together, the electrostatic force will increase, since it is inversely proportional to the square of the distance between the objects. The gravitational force will also increase, but since gravitational force is weaker than the electrostatic force, the electrostatic force will dominate and cause the objects to repel each other more strongly. When the objects are moved farther apart, both the electrostatic and gravitational forces will decrease in the same manner, as both forces are inversely proportional to the square of the distance. However, the electrostatic force will still dominate, and the objects will continue to repel each other. In conclusion, if the electrostatic force acting between two positively charged objects is exactly the same as the gravitational force, the objects would neither attract nor repel each other. When the distance between the objects is changed, the electrostatic force will dominate, causing the objects to repel each other more strongly when they are closer and less strongly when they are farther apart.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coulomb's Law

Coulomb's Law is a fundamental principle in physics that describes the electrostatic force between two charged particles. Mathematically, it is expressed as \( F_e = \frac{k \cdot |q1 \cdot q2|}{r^2} \), where \( F_e \) is the electrostatic force, \( k \) is the Coulomb constant (\({8.99 \times 10^9} \( \frac{N \cdot m^2}{C^2} \)\)), \( q1 \) and \( q2 \) are the magnitudes of the electric charges, and \( r \) is the distance between the two charges.

This law implies that the force is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them. In simpler terms, charges with greater magnitude or closer proximity will result in stronger electrostatic forces. Understanding Coulomb's Law is essential for analyzing many electrical phenomena, including the scenario in which electrostatic and gravitational forces are balanced.

Newton's Law of Gravitation

Newton's Law of Gravitation explains the gravitational attraction between two masses. It is given by the equation \( F_g = \frac{G \cdot m1 \cdot m2}{r^2} \), where \( F_g \) represents the gravitational force, \( G \) is the gravitational constant (\({6.674 \times 10^{-11}} \( \frac{N \cdot m^2}{kg^2} \)\)), and \( m1 \) and \( m2 \) are the masses of the objects. Like Coulomb's Law, gravity also follows an inverse square law with distance.

The formula showcases that larger masses exert stronger gravitational pulls, whereas increasing distance weakens the gravitational attraction. Newton's Law of Gravitation helps us to understand the motion of planets, the behavior of objects on Earth, and it's instrumental in comparing and contrasting different types of forces in the universe.

Forces in Physics

Forces in physics are interactions that can change the motion of an object or maintain it in equilibrium. They come in various forms, such as gravitational, electrostatic, frictional, and magnetic forces, to name a few. Each force operates under specific principles and mathematical laws that govern their magnitudes and directions.

Understanding the different forces allows us to predict how objects will behave under various circumstances. For instance, in our exercise, we see how electric and gravitational forces can influence each other, leading to either attraction or repulsion between objects depending on their properties like mass, charge, and distance.

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges: positive and negative. Like charges repel each other, while opposite charges attract. Coulomb's Law specifically addresses the force between charged particles, which varies based on the magnitude of charges and distance between them.

Understanding electric charge is crucial when dealing with electrostatic phenomena, as it directly influences the strength and direction of the electrostatic force. This concept is integral to explaining why two positively charged objects in our exercise would repel each other if not balanced by an equal gravitational force.

Mass and Distance Relationship

The relationship between mass and distance plays a pivotal role in determining the force between objects, be it gravitational or electrostatic. As per Newton's and Coulomb's laws, both forces vary inversely with the square of the distance between objects, meaning that as the distance increases, the force of attraction or repulsion decreases rapidly.

However, the relationship to mass is different for gravitational force—where larger masses result in stronger attractions—while electric charge dictates the strength of electrostatic forces. This distinction is vital in understanding why, in our exercise, moving charged objects closer will dramatically affect the electrostatic force but only minimally change the gravitational force due to the much smaller coefficient of gravitational force (\( G \) versus \( k \) in Coulomb's Law).

In otherwise empty space, what would happen if the size of the clectrostatic force acting between two positively charged objects was exactly the same as that of the gravitational force acting between them? What would happen if they were moved closer together or farther apart?

Short Answer

Step by step solution

Identify the formulas for electrostatic and gravitational forces

Set electrostatic force equal to gravitational force

Analyze the change of forces when the distance changes

Key Concepts

Coulomb's Law

Newton's Law of Gravitation

Forces in Physics

Electric Charge

Mass and Distance Relationship

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Wave Optics

Physical Quantities And Units

Force

Scientific Method Physics

Energy Physics

Study anywhere. Anytime. Across all devices.