/*! 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} Problem 60 A conductor in electrostatic equ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 16: Problem 60

A conductor in electrostatic equilibrium contains a cavity in which there are two point charges: \(q_{1}=+5 \mu \mathrm{C}\) and \(q_{2}=-12 \mu \mathrm{C} .\) The conductor itself carries a net charge \(-4 \mu C .\) How much charge is on (a) the inner surface of the conductor? (b) the outer surface of the conductor?

Short Answer

Expert verified
Answer: The charge on the inner surface of the conductor is -7渭C and the charge on the outer surface of the conductor is 3渭C.

Step by step solution

01

Calculate the total charge inside the conductor cavity

We have two point charges inside the cavity: \(q_1=+5\mu C\) and \(q_2=-12\mu C\). To find the total charge inside the cavity, add these point charges together: $$Q_\text{cavity} = q_1 + q_2 = (+5\mu C) + (-12\mu C) = -7\mu C$$
02

Calculate the charge on the inner surface of the conductor

Since the total charge inside the cavity will equal the charge induced on the inner surface of the cavity, the charge on the inner surface of the conductor is: $$Q_\text{inner} = Q_\text{cavity} = -7\mu C$$
03

Calculate the charge on the outer surface of the conductor

To find the charge on the outer surface of the conductor, we need to consider that the net charge on the conductor is \(-4\mu C\). Since the charge on the inner surface has already been determined, the charge on the outer surface can be found as follows: $$Q_\text{outer} = Q_\text{total} - Q_\text{inner} = (-4\mu C) - (-7\mu C) = 3\mu C$$ The charge on the inner surface of the conductor is \(-7\mu C\), and the charge on the outer surface of the conductor is \(3\mu C\).

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

\(\mathrm{A} \mathrm{K}^{+}\) ion and a \(\mathrm{Cl}^{-}\) ion are directly across from each other on opposite sides of a membrane 9.0 nm thick. What is the electric force on the \(\mathrm{K}^{+}\) ion due to the \(\mathrm{Cl}^{-}\) ion? Ignore the presence of other charges.
A thin, flat sheet of charge has a uniform surface charge density \(\sigma(\sigma / 2\) on each side). (a) Sketch the field lines due to the sheet. (b) Sketch the field lines for an infinitely large sheet with the same charge density. (c) For the infinite sheet, how does the field strength depend on the distance from the sheet? [Hint: Refer to your field line sketch.J (d) For points close to the finite sheet and far from its edges, can the sheet be approximated by an infinitely large sheet? [Hint: Again, refer to the field line sketches.] (e) Use Gauss's law to show that the magnitude of the electric field near a sheet of uniform charge density \(\sigma\) is $E=\sigma /\left(2 \epsilon_{0}\right)$
What is the ratio of the electric force to the gravitational force between a proton and an electron separated by \(5.3 \times 10^{-11} \mathrm{~m}\) (the radius of a hydrogen atom)?

A metal sphere A has charge \(Q\). Two other spheres, B and \(\mathrm{C},\) are identical to \(\mathrm{A}\) except they have zero net charge. A touches \(\mathrm{B}\), then the two spheres are separated. B touches \(C\), then those spheres are separated. Finally, C touches A and those two spheres are separated. How much charge is on each sphere?
Three equal charges are placed on three corners of a square. If the force that \(Q_{\mathrm{a}}\) exerts on \(Q_{\mathrm{b}}\) has magnitude \(F_{\mathrm{ba}}\) and the force that \(Q_{\mathrm{a}}\) exerts on \(Q_{\mathrm{c}}\) has magnitude \(F_{\mathrm{ca}},\) what is the ratio of \(F_{\mathrm{ca}}\) to $F_{\mathrm{ba}} ?$
See all solutions

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Read Explanation

Torque and Rotational Motion

Read Explanation

Space Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Waves Physics

Read Explanation

Classical Mechanics

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.