Coulomb's Law: Videos & Practice Problems

Coulomb's Law is essential for understanding the forces between charged particles, as it allows the calculation of potential energy, which is proportional to the magnitude of the charges and inversely proportional to the distance between them. The law's formula is:

$E=k\frac{Q_1{Q}_2}{r^2}$

where E represents the potential energy or force, k is the permittivity constant ($9.0\times {10}^9 N·m^2/C^2$), Q1 and Q2 are the charges of the particles, and r is the distance between the ion centers in meters. The absolute charge of an ion is $1.602\times {10}^{-19} C$. This relationship indicates that a greater potential energy corresponds to a stronger ionic bond. Understanding Coulomb's Law is crucial for predicting the behavior of ionic compounds and the strength of their bonds.

Coulomb's Law Concept 1

Coulomb's law describes the interaction between charged particles, specifically the forces of attraction and repulsion that arise due to their electric charges. The fundamental formula for Coulomb's law is given by:

\( F = k \frac{|q_1 q_2|}{r^2} \)

In this equation, \( F \) represents the force between the charges, \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the centers of the two charges.

From Coulomb's law, we can derive insights into potential energy (\( U \)) between two charged particles, which is expressed as:

\( U = k \frac{q_1 q_2}{r} \)

This equation indicates that the potential energy is directly proportional to the product of the charges (\( q_1 \) and \( q_2 \)). Therefore, as the magnitude of the charges increases, the potential energy also increases. Conversely, potential energy is inversely proportional to the distance (\( r \)) between the charges; thus, as the distance increases, the potential energy decreases.

Understanding these relationships is crucial, as a higher potential energy correlates with a stronger ionic bond between oppositely charged particles. This foundational knowledge of Coulomb's law is essential for exploring further concepts in electrostatics and chemical bonding.

Coulomb's Law Concept 2

Coulomb's law describes the electrostatic force between two charged particles. The formula for Coulomb's law can be expressed as:

\( F = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q_1 Q_2}{R^2} \)

In this equation, \( F \) represents the force in newtons, \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges in coulombs, and \( R \) is the distance between the centers of the two charges in meters. The constant \( \epsilon_0 \), known as the permittivity of free space, is approximately \( 9.0 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \).

It's important to note that the absolute charge of a single ion is \( 1.602 \times 10^{-19} \) coulombs. For example, if an ion has a charge of +2, its total charge in coulombs can be calculated by multiplying the absolute charge by 2, resulting in:

\( 2 \times 1.602 \times 10^{-19} \, \text{C} = 3.204 \times 10^{-19} \, \text{C} \)

Understanding these concepts is crucial for solving problems related to electrostatics and the interactions between charged particles.

Coulomb's Law Example

When two charged particles are placed in proximity to each other, they exert a force of attraction or repulsion depending on their charges. In this case, a positive charge of \(4.13 \times 10^{-19}\) coulombs and a negative charge of \(3.37 \times 10^{-17}\) coulombs are separated by a distance of \(8.03 \times 10^{-7}\) meters. Since the charges are of opposite signs, they will attract each other.

The force of attraction can be calculated using Coulomb's Law, which is expressed as:

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

Here, \(F\) is the force between the charges, \(k\) is the Coulomb's constant (\(9.0 \times 10^9 \, \text{N m}^2/\text{C}^2\)), \(q_1\) and \(q_2\) are the magnitudes of the charges, and \(r\) is the distance between the charges.

Substituting the values into the equation:

F = 9.0 \times 10^9 \cdot \frac{|4.13 \times 10^{-19} \cdot (-3.37 \times 10^{-17})|}{(8.03 \times 10^{-7})^2}

Calculating this gives a force of attraction of approximately \(-1.94 \times 10^{-13}\) newtons. The negative sign indicates that the force is attractive, confirming the principle that opposite charges attract each other.

A force of 3.24 x 10^-12 N exists between a +3 charge and another charged particle. The ions are 2.53 x 10^-8 m apart. What is the charge of the unknown charged particle?  (Rework numbers since you went from +15 to +3)

• A. 4.79 x 10^-19 C
• B. 7.59 x 10^-18 C
• C. 5.89 x 10^-18 C
• D. 4.12 x 10^-19 C

Answer: (A)

Here’s what students ask on this topic:

What is Coulomb's law?

Coulomb's Law is a fundamental principle in physics, named after the French physicist Charles-Augustin de Coulomb who introduced it in the 1780s. It describes the force between two charged objects. According to Coulomb's Law, the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between their centers.

The law is often expressed by the equation:

F = k * (|q₁ * q₂| / r²)

where:

• F is the force,
• q₁ and q₂ are the charges,
• r is the distance,
• k is Coulomb's constant (8.9875 x 10⁹ Nm²/C² in vacuum).

The force is attractive if the charges have opposite signs and repulsive if they have the same sign. Coulomb's Law is a cornerstone in the study of electrostatics and plays a crucial role in understanding the interactions between charged particles.

What is "k" in Coulomb's law?

In Coulomb's Law, "k" represents the Coulomb's constant, which is a proportionality factor that helps to determine the magnitude of the electrostatic force between two point charges. The value of "k" depends on the medium in which the charges are located and the units used for measurement. In a vacuum, "k" is approximately equal to 8.9875 × 10⁹ N m²/C² when using the International System of Units (SI). This constant arises from the equation:

$F=k\cdot \frac{|q_1\cdot q_2|}{r^2}$

where F is the force between charges, q₁ and q₂ are the magnitudes of the charges, and r is the distance between the centers of the two charges. Coulomb's constant allows us to calculate the force of attraction or repulsion between two charged particles accurately.

What are q₁ and q₂ in Coulomb's law?

In Coulomb's law, Q₁ and Q₂ represent the magnitudes of electric charges on two point charges for which you are calculating the electrostatic force between them. The law states that the electrostatic force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (Q₁ and Q₂) and inversely proportional to the square of the distance (r) between their centers. The formula is given by:

$F=k\frac{|Q{}_1\cdot Q{}_2|}{r^2}$

Here, k is Coulomb's constant (approximately $8.9875\times {10}^9 N·m^2/C^2$ in a vacuum), and r is the distance between

What is Coulomb's law used for?

Coulomb's law is a fundamental principle in physics that quantifies the electric force between two charged objects. It states that the force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q₁ and q₂), and inversely proportional to the square of the distance (r) between their centers. The law is mathematically expressed as:

$F=k\cdot |q{}_1\cdot q{}_2|/r^2$

where k is Coulomb's constant.

Coulomb's law is used to calculate the magnitude and direction of the electrostatic force in various applications, such as determining the strength of the electric field generated by a particular charge distribution, analyzing the forces between charged particles in atomic and molecular systems, and in the design of electrical equipment and circuits. It is also essential for understanding concepts like electric potential energy and is foundational for studies in electromagnetism and electronics.