Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 26: Q. 51 (page 739)

The potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity. How much excess charge is on the sphere?

Short Answer

Expert verified

The excess charge is on the sphere is 1.1nC .

Step by step solution

01

Given Information

We have given that the potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity.

02

Simplify

The sphere is conductive, the potential will be the same throughout the volume, and will be equal to the potential at the surface of the sphere. The potential created by charge

V=kqr,

Where r is the given radius of the sphere. and solve for the charge as

localid="1648562464911" q=Vrk,

Substituting radius with diameter

q=Vd2k

Using the numerical values

localid="1649261072160" q=500·0.042·9·109=1.1nC

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

Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field Eout outside the sphere(r≥R) is simply that of a point charge Q. In Chapter 24, we used Gauss's law to find that the electric field Ein inside the sphere(r≤R) is radially outward with field strength

Ein=14πϵ0QR3r

a. The electric potential Voutoutside the sphere is that of a point charge Q. Find an expression for the electric potentialVinat position r inside the sphere. As a reference, let Vin=Voutat the surface of the sphere.

b. What is the ratio Vcenter/Vsurface?

c. Graph V versus r for 0 ≤r ≤3 R.

Initially, the switch in FIGUREP26.61is in position A and capacitors C2and C3are uncharged. Then the switch is flipped to position B. Afterward, what are the charge on and the potential difference across each capacitor?

Capacitors C1=10μFand C2=20μFare each charged to 10V, then disconnected from the battery without changing the charge on the capacitor plates. The two capacitors are then connected in parallel, with the positive plate of C1connected to the negative plate of C2and vice versa. Afterward, what are the charge on and the potential difference across each capacitor?

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE P26.66. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius R1while the outer conductor of radius R2is grounded (i.e., at V=0V). An insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the capacitance per meter of a coaxial cable. Assume that the insulating material between the cylinders is air.

b. Evaluate the capacitance per meter of a cable having R1=0.50mmand R2=3.0mm.

What are the magnitude and direction of the electric field at the dot in Figure EX26.7?
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Electrostatics

Read Explanation

Solid State Physics

Read Explanation

Dynamics

Read Explanation

Modern 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.

Sign-up for free