Chapter 23: Problem 16
Two stationary point charges \(+\)3.00 nC and \(+\)2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the \(+\)3.00-nC charge?
Short Answer
Step by step solution
Identify Known Values
Setup Coulomb's Law
Calculate Final Electric Potential Energy
Use Energy Conservation
Calculate the Speed
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Coulomb's Law
- \( F = \frac{k_e \cdot |q_1 \cdot q_2|}{r^2} \)
Understanding this law is key to solving problems concerning the interaction of charged particles, allowing us to calculate the force and potential energy between them.
Electric Potential Energy
For a point charge \( q \) in the presence of another charge \( Q \), the electric potential energy \( U \) can be calculated using:
- \( U = \frac{k_e \cdot Q \cdot q}{r} \)
In problems like the current one, we assess the initial and final potential energy when a charged particle moves between two points. The change in electric potential energy is crucial for understanding how kinetic energy varies as the particle moves.
Conservation of Energy
In this context, when an electron is released from rest, the electric potential energy it initially possesses transforms into kinetic energy as it gains speed moving through the electric field. The mathematical expression for this conservation is:
- \( \Delta U = U_i - U_f = K \)
- \( K = \frac{1}{2}mv^2 \)
Motion of Charged Particles
In this exercise, when the electron is released, it accelerates due to the attractive forces from the positively charged particles.
Analyzing the motion involves understanding how the initial potential energy landscape changes as the electron moves. By calculating the shift in energy, we determine the velocity the electron acquires as it travels to a new position.
- Knowing the distance and energies involved lets us predict the path and speed the electron attains.