Question

Two positively charged particles are first brought close together and then released. Once released, the repulsion between particles causes them to move away from each other. (a) This is an example of potential energy being converted into what form of energy? (b) Does the potential energy of the two particles prior to release increase or decrease as the distance between them is increased.

Short answer

(a) The potential energy stored in the system is converted into kinetic energy when the particles are released. (b) The potential energy of the two particles prior to release decreases as the distance between them is increased.

Step-by-step solution

(a) Understanding the energy conversion

When the two positively charged particles are brought close together, there is potential energy stored in the system due to the electrostatic force between the particles. Once released, this potential energy is converted into another form of energy as the particles start moving. The conversion occurs as the repulsive force between the particles causes them to move away from each other. This movement indicates that the potential energy stored in the system is being converted into kinetic energy, which is the energy associated with the motion of the particles.

Answer for part (a)

The potential energy is converted into kinetic energy when the particles are released.

(b) Analyzing the potential energy and distance relationship

To analyze the relationship between potential energy and the distance between the positively charged particles, we need to consider the expression for electrostatic potential energy. The potential energy (PE) between two charged particles can be calculated using the formula: \(PE = k \frac{q_1 q_2}{r}\) where \(k\) is the electrostatic constant, \(q_1\) and \(q_2\) are the charges of the particles, and \(r\) is the distance between the particles. In this case, both the charges are positive, so the potential energy would be positive. Since the two particles are repelling each other, the potential energy would be maximum when the distance between them is minimum. As they move apart, the potential energy will decrease as the distance between them increases.

Answer for part (b)

The potential energy of the two particles prior to release decreases as the distance between them is increased.

Key concepts

Kinetic Energy

Kinetic energy is a fundamental concept in physics that refers to the energy an object possesses due to its motion. When two positively charged particles are initially held close together and then released, the energy dynamics of the system change. Initially, the charged particles have high potential energy due to their electrostatic repulsion. Once they start moving away from each other, this stored potential energy gets transformed into kinetic energy. Kinetic energy is given by the formula: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is the mass of the particle, and \( v \) is its velocity. As the particles accelerate away from each other due to repulsive forces, their velocities increase, meaning their kinetic energy also increases. This transformation is an essential mechanism in energy conservation, explaining how stored potential energy transitions into the energy of motion, exemplified by the moving particles.

Electrostatic Constant

The electrostatic constant, also known as Coulomb's constant, is a key factor in understanding the interactions between charged particles. It is denoted as \( k \) and has a value of approximately \( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \). This constant appears in Coulomb's law, which is used to calculate the electrostatic force between two charges. The formula that incorporates the electrostatic constant is:\[ F = k \frac{|q_1 q_2|}{r^2} \]where \( F \) is the force between the charges \( q_1 \) and \( q_2 \), and \( r \) is the distance separating them. In addition to determining the strength of the force between charged particles, \( k \) also plays a role in calculating potential energy between charges through the formula: \[ PE = k \frac{q_1 q_2}{r} \]Here, \( PE \) represents electrostatic potential energy, which is directly related to the distance \( r \) and the magnitude of the charges. The electrostatic constant is an integral part of assessing both the dynamics and energy configurations in systems with charged particles.

Charged Particles Interaction

Charged particles interact through electrostatic forces, which can be either attractive or repulsive. In the scenario where two positively charged particles are brought close to each other, they experience a repulsive force. This force originates due to the like charges that cause them to push away from each other. The law governing these interactions is known as Coulomb's law, dictating that like charges repel and opposite charges attract. The intensity of the force depends on:

• The magnitude of the charges, \( q_1 \) and \( q_2 \)
• The distance \( r \) separating the charges

The relationship is encapsulated in the formula mentioned earlier, where the force is \[ F = k \frac{|q_1 q_2|}{r^2} \]As charged particles move under the influence of these forces, their potential energy changes. When particles move apart due to repulsion, the potential energy decreases, leading to an increase in kinetic energy as discussed earlier. Understanding charged particles interactions is crucial for explaining the behavior of particles in electric fields and the movement observed when they are released from proximity.