Physics For Scientists And Engineers
Physics For Scientists And Engineers
4th Edition
ISBN: 9780134454016
Author: Randall D. Knight
Publisher: PEARSON
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Textbook Question
Chapter 25, Problem 1CQ

a. Charge q1is distance r from a positive point charge Q. Charge q2= q1/3 is distance 2r from Q. What is the ratio U1/U2 of their potential energies due to their interactions with Q? b. Charge q1is distance s from the negative plate of a parallel-plate capacitor. Charge q2= q1/3 is distance 2s from the negative plate. What is the ratio U1/U2 of their potential energies?

Expert Solution & Answer
Check Mark
To determine

a. Ratio of potential energy (U1/U2)

b. Ratio of potential energy (U1/U2)

Answer to Problem 1CQ

Solution:

a. Ratio of the potential energy is 6/1

b. Ratio of the potential energy is 6/1

Explanation of Solution

Given:

(a)

Charge q1 is at distance r from the positive point charge Q

Charge q2=q1/3 is at distance 2r from the positive point charge Q

(b)

Charge q1 is at distance s from the negative plate charge Q

Charge q2=q1/3 is at distance 2s from the negative plate charge Q

Formula used:

The potential energy of the charge particle is given by the formula

U=14πεo×q1Qr

Here,

U is the potential energy

εo is electric permissibility

q1&Q are charges

r is the distance between charge particles

Calculation:

(a)

Consider the diagram of the charge particles

Physics For Scientists And Engineers, Chapter 25, Problem 1CQ , additional homework tip  1

Figure.1

The potential energy of the charge particle q1 is given as

U1=14πεo×q1Qr …… (1)

The potential energy of the charge particle q2 is given as

U2=14πεo×q2Qr

Plugging the values in the above equation

U2=14πεo×q1Q3(2r) …… (2)

Calculate the ratio of the potential energy by dividing Eq. (1) by Eq. (2)

U1U2=14πεo×q1Qr14πεo×q1Q3(2r)U1U2=61

Hence the ration of their potential energy is 6:1.

(b)

Consider the diagram of the charge particles

Physics For Scientists And Engineers, Chapter 25, Problem 1CQ , additional homework tip  2

Figure.1

The potential energy of the charge particle q1 is given as

U1=14πεo×q1Qr

Plugging the values in the above equation

U1=14πεo×q1(Q)s …… (3)

The potential energy of the charge particle q2 is given as

U2=14πεo×q2Qr

Plugging the values in the above equation

U2=14πεo×q1(Q)3(2s) …… (4)

Calculate the ratio of the potential energy by dividing Eq. (3) by Eq. (4)

U1U2=14πεo×q1(Q)s14πεo×q1(Q)3(2s)U1U2=61

Hence the ration of their potential energy is 6:1.

Conclusion:

a. Ratio of the potential energy is 6/1

b. Ratio of the potential energy is 6/1

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02:09

Chapter 25 Solutions

Physics For Scientists And Engineers

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