Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q84P (page 719)

A small sphere with mass m carries a positive charge q and is attached to one end of a silk fiber of length L. The other end of the fiber is attached to a large vertical insulating sheet that has a positive surface charge density s. Show that when the sphere

is in equilibrium, the fiber makes an angle equal to arctan(σq2εomg)with the vertical sheet.

Short Answer

Expert verified

Proven below

Step by step solution

01

Step 1:

Required: Proven thatθ=arctanσq2εomg

02

Figure

03

Calculation

The electric field of the infinite sheet is given by

E=σ2εo (1)

So the force acting on the ball is given by

F=E=σq2εo (2)

The electric force is equal to the tension component

Tsin(θ)=σq2εo (3)

And the vertical component is equal to the weight

Tsin(θ)=mg (4)

Dividing (3) on (4) to get

tan(θ)=σq2mgεo⇒θ=arctanσq2εomg

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

Each of the lettered points at the corners of the cube in Fig. Q27.12 represents a positive charge qmoving with a velocity of magnitude vin the direction indicated. The region in the figure is in a uniform magnetic field , parallel to the x-axis and directed toward the right. Which charges experience a force due to B⇀? What is the direction of the force on each charge?

Question: A conducting sphere is placed between two charged parallel plates such as those shown in Figure. Does the electric field inside the sphere depend on precisely where between the plates the sphere is placed? What about the electric potential inside the sphere? Do the answers to these questions depend on whether or not there is a net charge on the sphere? Explain your reasoning.

An alpha particle (a He nucleus containing two protons and two neutrons and having a mass of 6.64×10-7kg) travelling horizontally at 35.6km/senter a uniform, vertical,1.80-T magnetic field.(a) What is the diameter of the path followed by this alpha particle? (b) what effect does the magnetic field have on the speed of the particle? (c) What are the magnitude and direction of the acceleration of the alpha particle while it is in the magnetic field? (d) explain why the speed of the particle does not change even though an unbalanced external force acts on it.

A fuse is a device designed to break a circuit, usually by melting when the current exceeds a certain value. What characteristics should the material of the fuse have?

A 5.00-A current runs through a 12-gauge copper wire (diameter

2.05 mm) and through a light bulb. Copper has8.5×108free electrons per

cubic meter. (a) How many electrons pass through the light bulb each

second? (b) What is the current density in the wire? (c) At what speed does

a typical electron pass by any given point in the wire? (d) If you were to use

wire of twice the diameter, which of the above answers would change?

Would they increase or decrease?
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Magnetism

Read Explanation

Electricity and Magnetism

Read Explanation

Force

Read Explanation

Electricity

Read Explanation

Magnetism and Electromagnetic Induction

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