Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 24: Q72P (page 715)

The magnitude E of an electric field depends on the radial distance r according toE=A/r4, where is a constant with the unit volt–cubic meter. As a multiple of A, what is the magnitude of the electric potential difference betweenr=2.00mandr=3.00m?

Short Answer

Expert verified

The magnitude of the electric potential difference isV(r)=+2.93×10−2A .

Step by step solution

01

Given data:

The intensity of the electric fieldE=Ar4,

The value of distance are r1=2.0mand r2=3.0m

02

Understanding the concept

Use the relation between the electric field E and potential Vas given below.

role="math" localid="1662730170007" E=−dVdr

Here,r is the distance.

03

Calculate the magnitude of the electric potential difference between r= 2.00 m and r= 3.00 m:

Since, the electric field is,

E=−dVdr∫∞rdV=−∫ηnEdrV(r)−V(∞)=∫ηnAr4dr

As V∞=0, then

V(r)=−Ar3−3r1r2=−A31r23−1r13=−A3133−123=+2.93×10−2A

V(r)=+A(0.029/m3)

Hence,the magnitude of the electric potential difference is +2.93×10−2A.

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 are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius 0.15 mwhose potential is 200 V(with V = 0at infinity)?

A positron (charge +e, mass equal to the electron mass) is moving at 1.0x107 m/sin the positive direction of an xaxis when, at x=0, it encounters an electric field directed along the xaxis. The electric potential Vassociated with the field is given in Fig. 24-57. The scale of the vertical axis is set by Vs=500.0 V. (a) Does the positron emerge from the field at x=0(which means its motion is reversed) or at x=0.50 m(which means its motion is not reversed)? (b) What is its speed when it emerges?

Question: An electron is placed in an x-yplane where the electric potential depends on xand yas shown, for the coordinate axes, in Fig. 24-51 (the potential does not depend on z). The scale of the vertical axis is set by Vs=500 V. In unit-vector notation, what is the electric force on the electron?

Question: In Fig. 24-48, what is the net electric potential at the origin due to the circular arc of charge Q1=+7.21pCand the two particles of chargesQ2=4.00Q1andQ3=-2.00Q1? The arc’s center of curvature is at the origin and its radius R is 2. 00 m; the angle indicated isθ=20.0°.

When an electron moves from A to B along an electric field line in Fig. 24-34, the electric field does 3.94 x 10-19 Jof work on it. What are the electric potential differences (a) VB - VA, (b) VC - VA, and (c) VC - VB?
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Turning Points in Physics

Read Explanation

Solid State Physics

Read Explanation

Engineering Physics

Read Explanation

Physics of Motion

Read Explanation

Mechanics and Materials

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