Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 31: Problem 7

It is speculated that isolated magnetic "charges" (magnetic monopoles) may exist somewhere in the universe. Which of Maxwell's equations, (1) Gauss's Law for Electric Fields, (2) Gauss's Law for Magnetic Fields, (3) Faraday's Law of Induction, and/or (4) the MaxwellAmpere Law, would be altered by the existence of magnetic monopoles? a) only (2) c) (2) and (3) b) (1) and (2) d) only (3)

Short Answer

Expert verified
Answer: a) only (2)

Step by step solution

01

Analyze Gauss's Law for Magnetic Fields

The Gauss's Law for Magnetic Fields states that the total magnetic flux through a closed surface is always zero. Mathematically, it is given by: \(\oint \vec{B} \cdot d\vec{A} = 0\) This equation implies that there are no isolated magnetic charges (monopoles) because the magnetic field lines form closed loops (i.e., they never begin or end within the volume enclosed by the surface). If magnetic monopoles were to exist, the magnetic flux through a closed surface enclosing a magnetic monopole would not be zero. Thus, the Gauss's Law for Magnetic Fields would be altered.
02

Analyze Gauss's Law for Electric Fields

The Gauss's Law for Electric Fields relates the electric flux through a closed surface to the charge enclosed within the surface. Mathematically, it is given by: \(\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}\) Since this equation deals with electric fields and charges, it would not be affected by the existence of magnetic monopoles.
03

Analyze Faraday's Law of Induction

Faraday's Law of Induction states that a time-varying magnetic field induces an electromotive force (EMF) in a closed loop. Mathematically, it is given by: \(\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}\) This equation relates the electric field to changes in the magnetic field but does not involve magnetic charges or monopoles. Thus, Faraday's Law of Induction would not be affected by the existence of magnetic monopoles.
04

Analyze Maxwell-Ampere Law

The Maxwell-Ampere Law relates the magnetic field around a closed loop to the electric current and time-varying electric field passing through the loop. Mathematically, it is given by: \(\oint \vec{B} \cdot d\vec{l} = \mu_0(I + \varepsilon_0 \frac{d\phi_E}{dt})\) This equation deals with the relationship between electric and magnetic fields, but does not involve magnetic charges or monopoles. Thus, the Maxwell-Ampere Law would not be affected by the existence of magnetic monopoles.
05

Choose the correct answer

Upon analyzing all of Maxwell's equations, we found that only Gauss's Law for Magnetic Fields would be altered by the existence of magnetic monopoles. Hence, the correct answer is: a) only (2)

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

Scientists have proposed using the radiation pressure of sunlight for travel to other planets in the Solar System. If the intensity of the electromagnetic radiation produced by the Sun is about \(1.40 \mathrm{~kW} / \mathrm{m}^{2}\) near the Earth, what size would a sail have to be to accelerate a spaceship with a mass of 10.0 metric tons at \(1.00 \mathrm{~m} / \mathrm{s}^{2} ?\) a) Assume that the sail absorbs all the incident radiation. b) Assume that the sail perfectly reflects all the incident radiation.

The voltage across a cylindrical conductor of radius \(r\), length \(L\), and resistance \(R\) varies with time. The timevarying voltage causes a time-varying current, \(i\), to flow in the cylinder. Show that the displacement current equals \(\epsilon_{0} \rho d i / d t,\) where \(\rho\) is the resistivity of the conductor.

Which of the following exerts the largest amount of radiation pressure? a) a \(1-\mathrm{mW}\) laser pointer on a \(2-\mathrm{mm}\) -diameter spot \(1 \mathrm{~m}\) away b) a 200-W light bulb on a 4 -mm-diameter spot \(10 \mathrm{~m}\) away c) a 100 -W light bulb on a 2 -mm-diameter spot 4 m away d) a 200 - \(\mathrm{W}\) light bulb on a 2 -mm-diameter spot \(5 \mathrm{~m}\) away e) All of the above exert the same pressure.

A tiny particle of density \(2000 . \mathrm{kg} / \mathrm{m}^{3}\) is at the same distance from the Sun as the Earth is \(\left(1.50 \cdot 10^{11} \mathrm{~m}\right)\). Assume that the particle is spherical and perfectly reflecting. What would its radius have to be for the outward radiation pressure on it to be \(1.00 \%\) of the inward gravitational attraction of the Sun? (Take the Sun's mass to be \(\left.2.00 \cdot 10^{30} \mathrm{~kg} .\right)\)

An electric field of magnitude \(200.0 \mathrm{~V} / \mathrm{m}\) is directed perpendicular to a circular planar surface with radius \(6.00 \mathrm{~cm}\). If the electric field increases at a rate of \(10.0 \mathrm{~V} /(\mathrm{m} \mathrm{s}),\) determine the magnitude and the direction of the magnetic field at a radial distance \(10.0 \mathrm{~cm}\) away from the center of the circular area.
See all solutions

Recommended explanations on Physics Textbooks

Electromagnetism

Read Explanation

Energy Physics

Read Explanation

Medical Physics

Read Explanation

Modern Physics

Read Explanation

Famous Physicists

Read Explanation

Mechanics and Materials

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