Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 21: Problem 3

If the flux of the gravitational field through a closed surface is zero, what can you conclude about the region interior to the surface?

Short Answer

Expert verified
If the flux of the gravitational field through a closed surface is zero, it implies that there is no mass present inside the surface.

Step by step solution

01

Understand the meaning of flux.

Flux refers to the total 'flow' of a field through a given surface. It is given by the surface integral of the field. This is usually represented mathematically as \( \oint \vec{F} \cdot d\vec{A} \)
02

Apply Gauss's law for gravity.

Gauss's law for gravity states that the flux of the gravitational field through a closed surface is equal to -4π times the mass enclosed by the surface. This can be represented as \( \oint \vec{G} \cdot d\vec{A} = -4πM_{enclosed} \)
03

Relate the given condition to Gauss's law

In this case, it's given that the flux through the closed surface is zero. This means that \( \oint \vec{G} \cdot d\vec{A} = 0 \). According to Gauss's law, this can only be true if the mass enclosed by the surface is zero, i.e. \( M_{enclosed}= 0 \)

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

An irregular conductor containing an irregular, empty cavity carries a net charge \(Q\). (a) Show that the electric field inside the cavity must be zero. (b) If you put a point charge inside the cavity, what value must it have in order to make the charge density on the outer surface of the conductor everywhere zero?

A study shows that mammalian red blood cells (RBCs) carry electric charge resulting from 4.4 million (rabbit cells) to 15 million (human cells) excess electrons spread over their surfaces. Approximating rabbit and human RBCs as spheres with radii \(30 \mu \mathrm{m}\) and \(36 \mu \mathrm{m},\) respectively, find the electric field strengths at the cells' surfaces.

A spherical shell of radius \(15 \mathrm{cm}\) carries \(4.8 \mu \mathrm{C}\) distributed uniformly over its surface. At the center of the shell is a point charge. (a) If the electric field at the sphere's surface is \(750 \mathrm{kN} / \mathrm{C}\) and points outward, what are (a) the point charge and (b) the field just inside the shell?

Why must the electric field be zero inside a conductor in electrostatic equilibrium?

A 250 -nC point charge is placed at the center of an uncharged spherical conducting shell \(20 \mathrm{cm}\) in radius. Find (a) the surface charge density on the outer surface of the shell and (b) the electric field strength at the shell's outer surface.
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Electricity and Magnetism

Read Explanation

Dynamics

Read Explanation

Oscillations

Read Explanation

Classical Mechanics

Read Explanation

Radiation

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