Question

Research suggests that the electric fields in some thunderstorm clouds can be on the order of \(10.0 \mathrm{kN} / \mathrm{C}\). Calculate the magnitude of the electric force acting on a particle with two excess electrons in the presence of a \(10.0-\mathrm{kN} / \mathrm{C}\) field.

Short answer

Answer: The magnitude of the electric force acting on the particle is 3.2 x 10^-15 N.

Step-by-step solution

Find the charge of the particle

We need to find the charge of the particle with two excess electrons. Since each electron has a charge of -1.6 x 10^-19 C (negative because the charge on an electron is negative), we can calculate the charge as follows: Charge = Number of excess electrons * Charge of one electron Charge = 2 * (-1.6 x 10^-19 C)

Calculate the charge of the particle

Now, we can calculate the charge of the particle: Charge = 2 * (-1.6 x 10^-19 C) Charge = -3.2 x 10^-19 C

Use the formula for electric force

We can use the formula for the electric force on a charged particle: Electric force = Charge * Electric field We are given the electric field as 10.0 kN/C (or 10,000 N/C). So, Electric force = -3.2 x 10^-19 C * 10,000 N/C

Calculate the electric force

Now we can calculate the electric force acting on the particle: Electric force = -3.2 x 10^-19 C * 10,000 N/C Electric force = -3.2 x 10^-15 N

Find the magnitude of the electric force

Since we are asked to find the magnitude of the electric force, we can ignore the negative sign: Magnitude of electric force = 3.2 x 10^-15 N The magnitude of the electric force acting on the particle in the given electric field is 3.2 x 10^-15 N.

Key concepts

Electric Fields

An electric field is a region around a charged particle or object within which an electric force is exerted on other charged particles or objects. This invisible field can be thought of much like the gravitational field of the Earth; it has a specific direction and magnitude that determines how it acts on objects within it. The concept of an electric field is crucial in understanding how and why charges interact with each other.

The strength of an electric field (\( E \)) is defined as the force (\( F \text{ormula} Electric force = \( |q| \times |E| \)

Using the magnitude of the electric force and charge, we can understand the behavior of charged particles within an electric field. This becomes particularly important in contexts such as electrical engineering, where controlling the motion of charges is essential, and in understanding natural phenomena like the electrical activity in thunderstorms.

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. Charges can be either positive or negative, and opposite charges attract each other while like charges repel each other. Objects can become charged in several ways, such as through the transfer of electrons, which are negatively charged particles.

The charge of a single electron is approximately \text{ormula} \( q_{particle} = n \times e \)

where \text{ormula} Electric force = q \times E \)

The charge of the particle interacts with the electric field, leading to the exertion of an electric force. If the charge has more electrons, as in the case of the particle in the problem, it will have a greater force acting upon it in an electric field of a given strength.

Coulomb's Law

Coulomb's Law is a fundamental principle of electromagnetism that describes the force between two point charges. It was first described by French physicist Charles-Augustin de Coulomb in the 18th century. The law states that the electric force between two stationary, point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

The formula is given by: \[ F = k \frac{|q_1 \times q_2|}{r^2} \]
where:

• \( F \) is the magnitude of the electric force between the charges,
• \( q_1 \) and \text{ormula} Electric force = \frac{k \times |q_1 \times q_2|}{r^2} \)
  
  In the context of the exercise, Coulomb's Law is not directly employed since we are dealing with a uniform electric field and a single charge, but understanding the law aids in comprehending the interaction between charges and why electric fields exist. Coulomb's Law is foundational in the study of electrostatics, impacting numerous applications in electronics, communication, and many other technology sectors.