Problem 44 How can we describe the force be... [FREE SOLUTION]

Chapter 6: Problem 44

How can we describe the force between two charged bodies?

Short Answer

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Question: Explain the process of describing the force between two charged bodies using Coulomb's Law. Answer: To describe the force between two charged bodies, we first need to understand the concept of electrostatic force, which is the interaction between charged particles. We then apply Coulomb's Law, a formula that states the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is: F = k (|q1 q2|/r^2), where F represents the electrostatic force, k is the electrostatic constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charged bodies. We also need to determine the direction of the force, which depends on the signs of the charges: repulsive if charges have the same sign and attractive if charges have opposite signs. Finally, we calculate the electrostatic force using the provided values and Coulomb's Law formula.

Step by step solution

Understand the concept of electrostatic force

The force between two charged bodies is called the electrostatic force. It is the force that causes charged particles to be repelled from or attracted to one another. Electrostatic force is a fundamental force in nature, and it plays a crucial role in many physical processes.

Introduce Coulomb's Law

Coulomb's Law is the formula that describes the electrostatic force between two charged bodies. It states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as: \[F = k \frac{|q_1 q_2|}{r^2}\] where: - F is the electrostatic force - k is the electrostatic constant, approximately equal to \(8.9875 脳 10^9 N m^2 C^{-2}\) - \(q_1\) and \(q_2\) are the magnitudes of the charges on the two bodies - r is the distance between the two charged bodies

Determine the direction of the force

The direction of the force depends on the signs of the charges. If both charges have the same sign (both positive or both negative), the force will be repulsive, meaning the charged bodies push away from each other. If the charges have opposite signs (one positive and one negative), the force will be attractive, meaning the charged bodies will pull towards each other.

Apply Coulomb's Law to calculate the force

Given the values of the charges \(q_1\) and \(q_2\) and the distance r between the two charged bodies, you can calculate the electrostatic force between them using Coulomb's Law. Simply plug in the values into the formula and solve for F: \[F = k \frac{|q_1 q_2|}{r^2}\] In summary, to describe the force between two charged bodies, we apply Coulomb's Law to calculate the magnitude of the electrostatic force and then determine its direction based on the signs of the charges.

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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 that helps us understand the force between charged bodies. It is named after Charles-Augustin de Coulomb, who discovered this relationship in the late 18th century. This law provides a mathematical formula to calculate the electrostatic force exerted between two point charges:

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

This equation explains how the force (F) between two charges is not only dependent on the amount of charge each particle has but also on the distance (r) separating them. As the distance increases, the force decreases quickly, being inversely proportional to the square of the distance. On the other hand, as the magnitude of the charges increases, the force between them grows directly proportionally.

Some important points about Coulomb's Law include:

The constant k, known as the electrostatic constant, is approximately 8.9875 脳 10^9 N m^2 C^{-2}. This constant is crucial for calculations, ensuring we have the correct units for force.
It applies to point charges, which are idealized charges concentrated at a single point.
Understanding the direction of the force is essential. Opposite charges attract, whereas like charges repel, which impacts how they behave in various contexts like electric fields.

Charged Particles

Charged particles are objects that carry an electric charge, either positive or negative. These charges are fundamental properties of particles, and they arise from an imbalance in the number of protons (positively charged) and electrons (negatively charged) in an atom or molecule. Charged particles can be found everywhere in the universe, from subatomic particles like electrons and protons to larger structures such as ions.

Here's what you need to know about charged particles:

**Types of charges**: There are two types of electric charges - positive and negative. Positive charges are typically found on protons, while negative charges are often associated with electrons.
**Interactions**: Charged particles interact with each other through electrostatic forces, described by Coulomb's Law. These interactions influence the way particles move and behave in electric fields and circuits.
**Role in electricity**: Charged particles are the building blocks of electricity. When they move, they create an electric current. This is the flow of electric charge, which powers our homes and technology.

Charged particles and their interactions are integral to understanding electricity and magnetism, both of which are indispensable in today's modern world.

Fundamental Forces

In physics, there are four fundamental forces that dictate how particles interact with each other. These forces are the cornerstones of almost all physical phenomena in the universe. Among these, the electrostatic force is just one part:

**Gravitational Force**: This is the force of attraction between two masses. It keeps planets in orbit and apples falling to the ground.
**Electromagnetic Force**: This force includes electrostatic and magnetic interactions. While the electrostatic force results from charged particles, magnetism arises from moving charges or intrinsic magnetic moments.
**Weak Nuclear Force**: Responsible for radioactive decay processes, this force plays a role in nuclear reactions in stars.
**Strong Nuclear Force**: This is the force that holds atomic nuclei together, countering the repulsion between protons due to their positive charge.

Among these fundamental forces, the electromagnetic force, which includes the electrostatic force, is crucial for everyday phenomena. It governs the behavior of charged particles, affecting everything from chemical bonds to electromagnetic waves. Understanding these forces provides insight into the very fabric of our universe.

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How can we describe the force between two charged bodies?

Short Answer

Step by step solution

Understand the concept of electrostatic force

Introduce Coulomb's Law

Determine the direction of the force

Apply Coulomb's Law to calculate the force

Key Concepts

Coulomb's Law

Charged Particles

Fundamental Forces

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