Physics
Magnetic Charge
Magnetic charge refers to a hypothetical property similar to electric charge, but associated with magnetic fields. In theory, magnetic charge would create magnetic fields in a manner analogous to how electric charge creates electric fields. However, magnetic monopoles, which would carry magnetic charge, have not been observed in nature, and the existence of magnetic charge remains a topic of theoretical interest in physics.
Written by Perlego with AI-assistance
Related key terms
1 of 5
12 Key excerpts on "Magnetic Charge"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
Before his formulation, the presence of electric charge was simply inserted into the equations of quantum mechanics (QM), but in 1931 Dirac showed that a discrete charge naturally falls out of QM. That is to say, we can maintain the form of Maxwell's equations and still have Magnetic Charges. Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product q e q m , and independent of the distance between them. Quantum mechanics dictates, however, that angular momentum is quantized in units of ħ , so therefore. the product q e q m must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized. What are the units in which Magnetic Charge would be quantized? Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He considered a point-like Magnetic Charge whose magnetic field behaves as q m / r 2 and is directed in the radial direction. Because the divergence of B is equal to zero almost everywhere, except for the locus of the magnetic monopole at r = 0, one can locally define the vector potential such that the curl of the vector potential A equals the magnetic field B . However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the northern hemisphere, and another set of functions for the southern hemispheres.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
The H-field, therefore, is analogous to the electric field E which starts at a positive charge and ends at a negative charge. It is tempting, therefore, to model magnets in terms of Magnetic Charges localized near the poles. Unfortunately, this model is incorrect; for instance, it often fails when determining the magnetic field inside of magnets. Magnetic monopole (hypothetical) A magnetic monopole is a hypothetical particle (or class of particles) that has, as its name suggests, only one magnetic pole (either a north pole or a south pole). In other words, it would possess a Magnetic Charge analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Modern interest in this concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence, or the possibility, of magnetic monopoles. These theories and others have inspired extensive efforts to search for monopoles. Despite these efforts, no magnetic monopole has been observed to date. In recent research, materials known as spin ices can simulate monopoles, but do not contain actual monopoles. The magnetic field and permanent magnets Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel, that have been magnetized, and they have both a north and a south pole. Magnetic field of permanent magnets The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The B field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m ). The equations are non-trivial and also depend on the distance from ______________________________ WORLD TECHNOLOGIES ______________________________ the magnet and the orientation of the magnet.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
That is to say, we can maintain the form of Maxwell's equations and still have Magnetic Charges. Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole. Classically, the electromagnetic field surro-unding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product q e q m , and independent of the distance between them. Quantum mechanics dictates, however, that angular momentum is quantized in units of ħ , so therefore. the product q e q m must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized. What are the units in which Magnetic Charge would be quantized? Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He consi-dered a point-like Magnetic Charge whose magnetic field behaves as q m / r 2 and is directed in the radial direction. Because the divergence of B is equal to zero almost everywhere, except for the locus of the magnetic monopole at r = 0, one can locally define the vector potential such that the curl of the vector potential A equals the magnetic field B . However, the vector potential cannot be defined globally precisely because the diver-gence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the northern hemisphere, and another set of functions for the southern hemispheres. These two vector potentials are matched at the equator, and they differ by a gauge transformation. The wave function of an electrically-charged particle (a probe charge) that orbits the equator generally changes by a phase, much like in the Aharonov–Bohm effect.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
The H-field, therefore, is analogous to the electric field E which starts at a positive charge and ends at a negative charge. It is tempting, therefore, to model magnets in terms of Magnetic Charges localized near the poles. Unfortunately, this model is incorrect; for instance, it often fails when determining the magnetic field inside of magnets. (See Non-uniform magnetic field causes like poles to repel and opposites to attract below.) Magnetic monopole (hypothetical) A magnetic monopole is a hypothetical particle (or class of particles) that has, as its name suggests, only one magnetic pole (either a north pole or a south pole). In other words, it would possess a Magnetic Charge analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Modern interest in this concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence, or the possibility, of magnetic monopoles. These theories and others have inspired extensive efforts to search for monopoles. Despite these efforts, no magnetic monopole has been observed to date. In recent research, materials known as spin ices can simulate monopoles, but do not contain actual monopoles. The magnetic field and permanent magnets Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel, that have been magnetized, and they have both a north and a south pole. Magnetic field of permanent magnets The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The B field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m ). The equations are non-trivial and also depend on the distance from the magnet and the orientation of the magnet.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
The H-field, therefore, is analogous to the electric field E which starts at a positive charge and ends at a negative charge. It is tempting, therefore, to model magnets in terms of Magnetic Charges localized near the poles. Unfortunately, this model is incorrect; for instance, it often fails when determining the magnetic field inside of magnets. Magnetic monopole (hypothetical) A magnetic monopole is a hypothetical particle (or class of particles) that has, as its name suggests, only one magnetic pole (either a north pole or a south pole). In other words, it would possess a Magnetic Charge analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Modern interest in this concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence, or the possibility, of magnetic monopoles. These theories and others have inspired extensive efforts to search for monopoles. Despite these efforts, no magnetic monopole has been observed to date. In recent research, materials known as spin ices can simulate monopoles, but do not contain actual monopoles. The magnetic field and permanent magnets Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel, that have been magnetized, and they have both a north and a south pole. Magnetic field of permanent magnets The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The B field of a small straight magnet is proportional to the magnet's strength ________________________ WORLD TECHNOLOGIES ________________________ (called its magnetic dipole moment m ). The equations are non-trivial and also depend on the distance from the magnet and the orientation of the magnet.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
That is to say, we can maintain the form of Maxwell's equations and still have Magnetic Charges. Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product q e q m , and independent of the distance between them. Quantum mechanics dictates, however, that angular momentum is quantized in units of ħ , so therefore. the product q e q m must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized. What are the units in which Magnetic Charge would be quantized? Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He considered a point-like Magnetic Charge whose magnetic field behaves as q m / r 2 and is directed in the radial direction. Because the divergence of B is equal to zero almost everywhere, except for the locus of the magnetic monopole at r = 0, one can locally define the vector potential such that the curl of the vector potential A equals the magnetic field B . However, the vector potential cannot be defined globally precisely because the div-ergence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the northern hemisphere, and another set of functions for the southern hemispheres. These two vector potentials are matched at the equator, and they differ by a gauge transformation. The wave function of an electrically-charged particle (a probe charge) that orbits the equator generally changes by a phase, much like in the Aharonov–Bohm effect.
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
6.1 Definition of the Magnetic Field 6.2 Some Properties of the Magnetic Field 6.3 Vector Potential 6.4 Field of Any Current-Carrying Wire 6.5 Fields of Rings and Coils 6.6 Change in B at a Current Sheet 6.7 How the Fields Transform 6.8 Rowland's Experiment 6.9 Electric Conduction in a Magnetic Field: The Hall Effect Problems THE MAGNETIC FIELD 208 214 220 223 226 231 235 241 241 245 208 CHAPTER SIX DEFINITION OF THE MAGNETIC FIELD 6.1 A charge which is moving parallel to a current of other charges experiences a force perpendicular to its own velocity. We can see it happening in the deflection of the electron beam in Fig. 5.3. We dis- covered in Section 5.9 that this is consistent with-indeed, is required by-Coulomb's law with charge invariance and special relativity. And we found that a force perpendicular to the charged particle's velocity also arises in motion at right angles to the current-carrying wire. For a given current the magnitude of the force, which we calculated for the particular case in Fig. 5.20a, is proportional to the product of the particle's charge q and its speed v in our frame. Just as we defined the electric field E as the vector force on unit charge at rest, so we can define another field B by the velocity-dependent part of the force that acts on a charge in motion. The defining relation was introduced at the beginning of Chapter 5. Let us state it again more carefully. At some instant t a particle of charge q passes the point (x, y, z) in our frame, moving with velocity v. At that moment the force on the particle (its rate of change of momentum) is F. The electric field at that time and place is known to be E. Then the magnetic field at that time and place is defined as the vector B which satisfies the vector equation F = qE + 1v X B c (1) Of course, F here includes only the charge-dependent force and not, for instance, the weight of the particle carrying the charge.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 6 Magnetic Monopole A magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole. In more technical terms, a magnetic monopole would have a net Magnetic Charge. Modern interest in the concept stems from particle theories, notably the grand unification and superstring theories, which predict their existence. The magnetic monopole was first hypothesized by Pierre Curie in 1894, but the quantum theory of Magnetic Charge started with a paper by the physicist Paul A.M. Dirac in 1931. In this paper, Dirac showed that the existence of magnetic monopoles was consistent with Maxwell's equations only if electric charges are quantized, which is always observed. Since then, several systematic monopole searches have been performed. Experiments in 1975 and 1982 produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive. The detection of magnetic monopoles is an open problem in experimental physics. Within theoretical physics, some modern approaches predict the existence of magnetic monopoles. Joseph Polchinski, a prominent string-theorist, described the existence of monopoles as one of the safest bets that one can make about physics not yet seen. These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive to be created in particle accelerators, and also too rare in the Universe to enter a particle detector with much probability. Some condensed matter systems propose a structure superficially similar to a magnetic monopole, known as a flux tube. The ends of a flux tube form a magnetic dipole, but since they move independently, they can be treated for many purposes as independent magnetic monopole quasiparticles.
eBook - PDFClassical Solutions in Quantum Field Theory
Solitons and Instantons in High Energy Physics
- Erick J. Weinberg(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
(5.3) In the rationalized natural units used here, Q M is the Magnetic Charge, with the factor of 4π included so that its definition parallels that of the electric charge Q E , which creates a Coulomb electric field E = Q E 4πr 2 ˆ r. (5.4) The auxiliary quantity g = Q M /4π has been introduced because it allows some equations to take on a simpler form. It should be noted that this usage is not universal in the literature, with some authors using definitions of electric and Magnetic Charges that differ by a factor of 4π. In standard treatments of electrodynamics it is useful to write the electric and magnetic fields in terms of potentials. In particular, the fact that B is divergence- less means that it can be written as the curl of a vector potential, B = ∇ × A. If there are Magnetic Charges, B is no longer divergenceless, and so cannot be globally written as a curl. However, if the Magnetic Charges were point-like, or at least confined to a finite volume, one might try to write B as a curl in the regions where Magnetic Charges were absent. Suppose, for example, that there were a point-like monopole at the origin with Magnetic Charge Q M = 4πg. Let us define a vector potential with Cartesian components A Ii = − ij3 ˆ r j g z + r (5.5) or spherical components 1 A I r = A I θ = 0, A I φ = g(cos θ − 1). (5.6) This has a singularity, known as a Dirac string, along the negative z-axis. How- ever, away from this singularity the curl of A I is equal to the Coulomb field of Eq. (5.3). The location of the string seems somewhat arbitrary. Indeed, the potential A IIi = − ij3 ˆ r j g z − r (5.7) or, equivalently, A II r = A II θ = 0, A II φ = g(cos θ + 1), (5.8) that has a Dirac string along the positive z-axis, yields the same magnetic field, apart from singularities along the strings. [Note, for later reference, that A I (r) = A II (−r).] The difference between these two potentials, 1 These are defined so that Axdx + Ay dy + Az dz = Ar dr + A θ dθ + A φ dφ.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
21.2 | The Force That a Magnetic Field Exerts on a Moving Charge 521 charge moves at an angle u* with respect to the field (see Figure 21.7c), only the velocity component v sin u, which is perpendicular to the field, gives rise to a magnetic force. This force F B is smaller than the maximum possible force. The component of the velocity that is parallel to the magnetic field yields no force. Figure 21.7 shows that the direction of the magnetic force F B is perpendicular to both the velocity v B and the magnetic field B B ; in other words, F B is perpendicular to the plane defined by v B and B B . As an aid in remembering the direction of the force, it is convenient to use Right-Hand Rule No. 1 (RHR-1), as Figure 21.8 illustrates: Right-Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field B B and the thumb points along the velocity v B of the charge. The palm of the hand then faces in the direction of the magnetic force F B that acts on a positive charge. It is as if the open palm of the right hand pushes on the positive charge in the direction of the magnetic force. If the moving charge is negative instead of positive, the direction of the magnetic force is opposite to that predicted by RHR-1. Thus, there is an easy method for finding the force on a moving negative charge. First, assume that the charge is positive and use RHR-1 to find the direction of the force. Then, reverse this direction to find the direction of the force acting on the negative charge. We will now use what we know about the magnetic force to define the magnetic field, in a procedure that is analogous to that used in Section 18.6 to define the electric field. Re- call that the electric field at any point in space is the force per unit charge that acts on a test charge q 0 placed at that point. In other words, to determine the electric field E B , we divide the electrostatic force F B by the charge q 0 : E B 5 F B / q 0 .
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
21.2 | The Force That a Magnetic Field Exerts on a Moving Charge 583 charge moves at an angle u* with respect to the field (see Figure 21.7c), only the velocity component v sin u, which is perpendicular to the field, gives rise to a magnetic force. This force F B is smaller than the maximum possible force. The component of the velocity that is parallel to the magnetic field yields no force. Figure 21.7 shows that the direction of the magnetic force F B is perpendicular to both the velocity v B and the magnetic field B B ; in other words, F B is perpendicular to the plane defined by v B and B B . As an aid in remembering the direction of the force, it is convenient to use Right-Hand Rule No. 1 (RHR-1), as Figure 21.8 illustrates: Right-Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field B B and the thumb points along the velocity v B of the charge. The palm of the hand then faces in the direction of the magnetic force F B that acts on a positive charge. It is as if the open palm of the right hand pushes on the positive charge in the direction of the magnetic force. If the moving charge is negative instead of positive, the direction of the magnetic force is opposite to that predicted by RHR-1. Thus, there is an easy method for finding the force on a moving negative charge. First, assume that the charge is positive and use RHR-1 to find the direction of the force. Then, reverse this direction to find the direction of the force acting on the negative charge. We will now use what we know about the magnetic force to define the magnetic field, in a procedure that is analogous to that used in Section 18.6 to define the electric field. Re- call that the electric field at any point in space is the force per unit charge that acts on a test charge q 0 placed at that point. In other words, to determine the electric field E B , we divide the electrostatic force F B by the charge q 0 : E B 5 F B / q 0 .
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
CHAPTER 21 Magnetic forces and magnetic fields LEARNING OBJECTIVES After reading this module, you should be able to: 21.1 define magnetic field 21.2 calculate the magnetic force on a moving charge in a magnetic field 21.3 analyse the motion of a charged particle in a magnetic field 21.4 describe how the masses of ions are determined using a mass spectrometer 21.5 calculate the magnetic force on a current in a magnetic field 21.6 calculate the torque on a current‐carrying coil 21.7 calculate magnetic fields produced by currents 21.8 apply Ampère’s law to calculate the magnetic field due to a steady current 21.9 describe magnetic materials. INTRODUCTION This beautiful display of light in the sky is known as the northern lights (aurora borealis). It occurs when charged particles, streaming from the sun, become trapped by the earth’s magnetic field. The particles collide with molecules in the upper atmosphere, and the result is the production of light. Magnetic forces and magnetic fields are the subjects of this chapter. Source: Suranga Weeratunga / 123RF.com 21.1 Magnetic fields LEARNING OBJECTIVE 21.1 Define magnetic field. FIGURE 21.1 The needle of a compass is a permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other. S N Permanent magnets have long been used in navigational compasses. As figure 21.1 illus- trates, the compass needle is a permanent magnet supported so it can rotate freely in a plane. When the compass is placed on a horizontal surface, the needle rotates until one end points approximately to the north. The end of the needle that points north is labelled the north magnetic pole; the opposite end is the south magnetic pole. Magnets can exert forces on each other. Figure 21.2 shows that the magnetic forces between north and south poles have the property that like poles repel each other, and unlike poles attract. This behaviour is similar to that of like and unlike electric charges.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
