Question

A point charge $q_{1}$ is held stationary at the origin. A second charge $q_{2}$ is placed at point $a,$ and the electric potential energy of the pair of charges is $+5.4 \times 10^{-8} \mathrm{J}$ . When the second charge is moved to point $b$ , the electric force on the charge does $-1.9 \times 10^{-8} \mathrm{J}$ of work. What is the electric potential energy of the pair of charges when the second charge is at point $b ?$

   A point charge $q_{1}$ is held stationary at the origin. A second charge $q_{2}$ is placed at point $a,$ and the electric potential energy of the pair of charges is $+5.4 \times 10^{-8} \mathrm{J}$ . When the second charge is moved to point $b$ , the electric force on the charge does $-1.9 \times 10^{-8} \mathrm{J}$ of work. What is the electric potential energy of the pair of charges when the second charge is at point $b ?$

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University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young, Roger… 12th Edition

Chapter 23, Problem 2

Instant Answer

Solved by Expert Mohit Khurana

03/22/2019

Step 1

We have two point charges, \( q_1 \) and \( q_2 \). The charge \( q_1 \) is stationary at the origin, and \( q_2 \) is initially at point \( a \). The electric potential energy of the system when \( q_2 \) is at point \( a \) is given as \( +5.4 \times 10^{-8} \, Show more…

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A point charge $q_{1}$ is held stationary at the origin. A second charge $q_{2}$ is placed at point $a,$ and the electric potential energy of the pair of charges is $+5.4 \times 10^{-8} \mathrm{J}$ . When the second charge is moved to point $b$ , the electric force on the charge does $-1.9 \times 10^{-8} \mathrm{J}$ of work. What is the electric potential energy of the pair of charges when the second charge is at point $b ?$

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Key Concepts

Electric Potential Energy

This is the energy associated with a configuration of point charges due to the electrostatic forces between them. It quantifies the work needed to assemble the charges from infinity to their specific positions, and it is typically calculated using the formula U = k*(q1*q2)/r, where k is Coulomb's constant, q1 and q2 are the point charges, and r is the distance between them.

Work Done by Conservative Forces

In electrostatics, the electric force is a conservative force, meaning that the work it performs when moving a charge from one point to another is equal to the negative change in electric potential energy of the system. This relationship, expressed as ?U = -W, allows us to determine how the potential energy of a system changes based on the work performed by the electric force during the displacement of charges.

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