Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

Chapter 22: Q. 49 (page 626)

Charge $q_{2}$ in FIGURE $P 22.49$ is in equilibrium. What is $q_{1}$ $?$

Short Answer

Expert verified

Charge is $- 20 nC$ .

Step by step solution

01

Calculation for force on charge

Two charged particles, one with a charge of $q_{1}$ .

And the other with a charge of $q_{2}$ , separated by a distance of $r$ .

The two particles exert forces on each other, with the force decreasing as the distance between them grows and increasing as the size of the charges increases.

$F_{C} = F_{1 on 2} = F_{2 on 1} = \frac{K |q_{1}| |q_{2}|}{r^{2}}$

Force for charge $q_{3}$ and $q_{2}$ :

${\vec{F}}_{32} = \frac{{Kq}_{3} q_{2}}{r_{32}^{2}}$

$= \frac{(9.0 \times 10^{9} N \cdot m^{2} / C^{2}) (5 \times 10^{- 9} C) q_{2}}{(0.1 m)^{2}}$

$= 4500 q_{2}$

02

Calculation of charge

Force for charge $q_{1}$ and $q_{2}$

${\vec{F}}_{12} = \frac{{Kq}_{1} q_{2}}{r_{12}^{2}}$

$= \frac{(9.0 \times 10^{9} N \cdot m^{2} / C^{2}) q_{1} q_{2}}{(0.2 m)^{2}}$

$= 225 \times 10^{9} q_{1} q_{2}$

{\vec{F}}_{12} = - {\vec{F}}_{32}

so,

${\vec{F}}_{12} = - {\vec{F}}_{32}$

$225 \times 10^{9} q_{1} q_{2} = - 4500 q_{2}$

$q_{1} = - \frac{4500}{225 \times 10^{9}}$

$q_{1} = - 20 \times 10^{- 9} C$

$q_{1} = - 20 nC$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What magnitude charge creates a 1.0 N/C electric field at a point 1.0 m away?

Figure showed how an electroscope becomes negatively charged. The leaves will also repel each other if you touch the electroscope with a positively charged glass rod. Use a series of charge diagrams to explain what happens and why the leaves repel each other.

The nucleus of $a^{125} X e$ atom (an isotope of the element xenon with mass $125 u$ ) is $6.0 f m$ in diameter. It has $54$ protons and charge $q = + 54 e .$

a. What is the electric force on a proton $2.0 f m$ from the surface of the nucleus?

b. What is the proton’s acceleration?

Hint: Treat the spherical nucleus as a point charge

What is the total charge of all the electrons in 1.0 L of liquid water?

In Section $22.3$ we claimed that a charged object exerts a net attractive force on an electric dipole. Let’s investigate this. FIGURE CP22.77 shows a permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is the distance r from the center of the dipole. We’ll assume, as is usually the case in practice, that s V r.

a. Write an expression for the net force exerted on the dipole by charge +Q.

b. Is this force toward +Q or away from +Q? Explain.

c. Use the binomial approximation $11 + x 2 - n \approx 1 -$ nx if x V 1 to show that your expression from part a can be written Fnet = 2KqQs/r3 .

d. How can an electric force have an inverse-cube dependence? Doesn’t Coulomb’s law say that the electric force depends on the inverse square of the distance? Explain.

See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Medical Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Electricity

Read Explanation

Wave Optics

Read Explanation

Dynamics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free