/*! 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. 75 The identical small spheres show... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 22: Q. 75 (page 628)

The identical small spheres shown in FIGURE CP22.75 are charged to +100 nC and -100nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

Short Answer

Expert verified

The mass of each sphere is4.1g.

Step by step solution

01

Given information

A free-body diagram for this is given below

02

Explanation

The net force on the given charge-100nCis the sum of the forces coming from the positive charge, gravity, and electric field. By resolving forces in the X direction, we get

鈭�Fx=FE-Fe-Tcos(90-胃)=0鈭�Fx=FE-Fe-Tcos80=0鈥�鈥�鈥�1

Resolving forces in the Y direction

role="math" localid="1648482100648" 鈭�Fy=Tsin80-FG=0鈥�鈥�2

Here we know that FG=mg

Now equation(2) becomes

T=mgsin80

Substitute above value in equation(1)

FE-Fe=Tcos80FE-Fe=sin80脳mg/cos80FE-Fe=mg/tan80

We know that

FE=qEFe=14蟺蔚0脳qQr2

Solving for mass m gives

qE-14蟺蔚0脳qQr2=mg/tan80m=qtan80gE-Q4蟺蔚0r2

m=100脳10-9脳tan809.8105-9脳109)100脳10-9sin210m=4.1g

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

The electric force on a charged particle in an electric field is F. What will be the force if the particle鈥檚 charge is tripled and the electric field strength is halved?

A 鈥�12nCcharge is located at 1x,y2=11.0cm,0cm2.What are the electric fields at the position 1x,y2=15.0cm,0cm2,1-5.0cm,0cm2,and10cm,5.0cm2? Write each electric field vector in component form.

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

You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air molecule. Most such collisions are elastic, so the electron collides, accelerates, collides, accelerates, and so on, gradually gaining speed. But if the electron鈥檚 kinetic energy just before a collision is 2.0脳10-18Jor more, it has sufficient energy to kick an electron out of the molecule it hits. Where there was one free electron, now there are two! Each of these can then accelerate, hit a molecule, and kick out another electron. Then there will be four free electrons. In other words, as FIGURE P22.61 shows, a sufficiently strong electric field causes a 鈥渃hain reaction鈥� of electron production. This is called a breakdown of the air. The current of moving electrons is what gives you the shock, and a spark is generated when the electrons recombine with the positive ions and give off excess energy as a burst of light.

  1. The average distance between ionizing collisions is 2.0渭m. (The electron鈥檚 mean free path is less than this, but most collisions are elastic collisions in which the electron bounces with no loss of energy.) What acceleration must an electron have to gain of kinetic energy in this distance?
  2. What force must act on an electron to give it the acceleration found in part a?
  3. What strength electric field will exert this much force on an electron? This is the breakdown field strength. Note: The measured breakdown field strength is a little less than your calculated value because our model of the process is a bit too simple. Even so, your calculated value is close.
  4. Suppose a free electron in air is 1.0 cm away from a point charge. What minimum charge is needed to cause a breakdown and create a spark as the electron moves toward the point charge?

44. What is the force F鈫� on the -1.0nC charge in the middle of FIGURE P22.44due to the four other charges? Give your answer in component form.
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Energy Physics

Read Explanation

Thermodynamics

Read Explanation

Mechanics and Materials

Read Explanation

Modern Physics

Read Explanation

Linear Momentum

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.