/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.15 The electric potential along the... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
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
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 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.
91影视
Discover

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

Find a degree

Magazine
Featured

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

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 26: Q.15 (page 738)

The electric potential along the x-axis is $V = 100 e^{- 2 x} V$ , where $x$ is in meters. What is $E_{x}$ at (a)role="math" localid="1649581712352" $x = 1.0 m$ and (b) role="math" localid="1649581719374" $x = 2.0 m$ ?

Short Answer

Expert verified

$(a) E_{x} = 27 V / m (b) E_{x} = 3.7 V / m$

Step by step solution

01

Given information and theory used

Given : The electric potential along the x-axis is : $V = 100 e^{- 2 x} V$

(a) $x = 1 . 0 m$ and (b) $x = 2.0 m$

Theory used :

The electric field is expressed as a function of potential as :

$E (x) = - \frac{d V (x)}{d x}$

02

Calculating Ex

The negative derivative of the potential $V = 100 e^{- 2 x} V$ is equivalent to the component of the electric field. As a result,

role="math" localid="1649581602113" $E (x) = - \frac{d V (x)}{d x} = - 100 (- 2 e^{- 2 x}) V / m = 200 e^{- 2 x} V / m$

(a) We have $E_{x} = 27 V / m at a = 1.0 m$ .

(a) We have $E_{x} = 3.7 V / m at x = 2.0 m$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

a. Use the methods of Chapter 25 to find the potential at distance $x$ on the axis of the charged rod shown in FIGURE P26.43.

b. Use the result of part a to find the electric field at distance $x$ on the axis of a rod

Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field $E_{out}$ outside the sphere $(r 鈮� R)$ is simply that of a point charge Q. In Chapter 24, we used Gauss's law to find that the electric field $E_{in}$ inside the sphere $(r 鈮� R)$ is radially outward with field strength

$E_{in} = \frac{1}{4 蟺系_{0}} \frac{Q}{R^{3}} r$

a. The electric potential $V_{out}$ outside the sphere is that of a point charge Q. Find an expression for the electric potential $V_{in}$ at position r inside the sphere. As a reference, let $V_{in} = V_{out}$ at the surface of the sphere.

b. What is the ratio $V_{center} / V_{surface} ?$

c. Graph V versus r for 0 $鈮�$ r $鈮�$ 3 R.

The electric potential along the $x - a x i s is V = 100 x^{2}$ V, where $x$ is in meters. What is $E_{x}$ at

(a) $x = 0 m$ and

(b) $x = 1 m$ ?

What are the magnitude and direction of the electric field at the dot in Figure EX26.8?

What is the equivalent capacitance of the three capacitors in Figure EX26.27?

See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Circular Motion and Gravitation

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Oscillations

Read Explanation

Atoms and Radioactivity

Read Explanation

Waves Physics

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.