Ch 23: Electric Potential

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 23: Electric Potential

Problem 16

Chapter 23, Problem 16

Two stationary point charges $positive 3.00$ nC and $positive 2.00$ 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 $positive 3.00$ -nC charge?

Verified step by step guidance

First, identify the initial and final positions of the electron. The electron starts at the midpoint between the two charges, which is 25.0 cm from each charge, and moves to a point 10.0 cm from the +3.00 nC charge.

Calculate the initial electric potential energy of the electron at the midpoint. Use the formula for electric potential energy: $ U = k \frac{q_1 q_2}{r} $, where $ k $ is Coulomb's constant, $ q_1 $ and $ q_2 $ are the charges, and $ r $ is the distance between them. Calculate the potential energy due to each charge and sum them.

Calculate the final electric potential energy of the electron when it is 10.0 cm from the +3.00 nC charge. Again, use the formula for electric potential energy for each charge and sum them.

Determine the change in electric potential energy as the electron moves from the midpoint to the final position. The change in potential energy is equal to the initial potential energy minus the final potential energy.

Use the conservation of energy principle to find the kinetic energy of the electron at the final position. The change in potential energy is equal to the change in kinetic energy. Use the formula $ KE = \frac{1}{2}mv^2 $ to solve for the speed $ v $ of the electron, where $ m $ is the mass of the electron.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Force

Electric force is the interaction between charged particles, described by Coulomb's law. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This concept is crucial for determining the forces acting on the electron due to the stationary charges.

Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. It is calculated based on the work done to move a charge within the field. Understanding this concept helps in determining the change in energy as the electron moves, which is essential for calculating its speed using energy conservation principles.

Conservation of Energy

The conservation of energy principle states that the total energy in a closed system remains constant. For the electron, its initial potential energy is converted into kinetic energy as it moves. By applying this principle, we can equate the initial potential energy to the kinetic energy at the given position to find the electron's speed.

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Related Practice

Textbook Question

A particle with charge $positive 4.20$ nC is in a uniform electric field $E$ directed to the left. The charge is released from rest and moves to the left; after it has moved $6.00$ cm, its kinetic energy is $+ 2.20 x 10^{- 6}$ J. What is the work done by the electric force?

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Textbook Question

Two protons are released from rest when they are $0.750$ nm apart. What is the maximum acceleration they will achieve and when does this acceleration occur?

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Textbook Question

A small particle has charge $negative 5.00$ $μ$ C and mass $2.00 \times 10^{- 4}$ kg. It moves from point $A$ , where the electric potential is $V sub A equals positive 200$ V, to point $B$ , where the electric potential is $V sub B equals positive 800$ V. The electric force is the only force acting on the particle. The particle has speed $5.00$ m/s at point $A$ . What is its speed at point $B$ ? Is it moving faster or slower at $B$ than at $A$ ? Explain.

Textbook Question

Two point charges of equal magnitude $Q$ are held a distance $d$ apart. Consider only points on the line passing through both charges. If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

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Textbook Question

Two point charges $q sub 1 equals positive 2.40$ nC and $q_{2} = - 6.50$ nC are $0.100$ m apart. Point $A$ is midway between them; point $B$ is $0.080$ m from $q sub 1$ and $0.060$ m from $q sub 2$ (Fig. E $23.19$ ). Take the electric potential to be zero at infinity. Find the potential at point $A$ .

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Textbook Question

Point charges $q sub 1 equals positive 2.00$ $μ$ C and $q_{2} = - 2.00$ $μ$ C are placed at adjacent corners of a square for which the length of each side is $3.00$ cm. Point $a$ is at the center of the square, and point $b$ is at the empty corner closest to $q sub 2$ $q sub 2$ . Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to $q sub 1$ and $q sub 2$ ?

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