Physics
Magnetic Flux Density
Magnetic flux density, also known as magnetic field strength, is a measure of the strength of a magnetic field. It is defined as the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. The SI unit for magnetic flux density is the tesla (T).
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10 Key excerpts on "Magnetic Flux Density"
eBook - PDF- Slawomir Tumanski(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
μ .and. magnetization. M .of.a.material . .In.free.space,.there.is.no. magnetization. and. permeability. is. equal. to. μ 0 ,. so. the. magnetic.flux. Φ .caused.by.a.magnetic.field. H .is . F = μ 0 A H . (2 .12) The unit of magnetic flux is 1 Wb (weber) or Vs . The.magnetic.flux.density. B .(sometimes.also.called.as. a.magnetic.induction).is.a.more.commonly.used.quan-tity.and.is.equal.to . B A = Φ . (2 .13) * . According. to. Einstein’s. theory. of. relativity,. for. the. stationary. observer,. this. statement. is. obvious,. but,. if. the. observer. is. mov-ing.with.the.charge,.the.effects.of.magnetic.and.electric.field.are. reversed. .So.we.can.say.that.the.magnetic.field.is.a.relativistic.cor-rection.to.the.electric.field.(see.Jiles.1998) . From.(2 .12) .and.(2 .13), .we.can.see.that.in.a.free.space.the. relationship.between.magnetic.field.strength. H .and.flux. density. B .is . B H = μ 0 . (2 .14) The unit of Magnetic Flux Density is 1 T (tesla) . The. presence. and. direction. of. magnetic. flux. can. be. easily.detected.with.iron.filings.(Figure.2 .3). According.to.Equation.2 .14, .in.a.free.space,.the.relation-ship.between.the.magnetic.field.strength. H .and.the.flux. density. B .is.linear.(constant.factor. μ 0 ). .For.this.reason,.it. does.not.matter.which.quantity.is.used.as.the.reference. source. .Independently.of.what.is.the.cause.and.what.is. the.result,.most.often,.the.flux.density.standard.is.used. as. a. reference. for. the. magnetic. field . . The. standard. is. defined.by.the.relationship.between.the.magnetic.field. generated.by.an.electric.current.and.mechanical.force . . A Magnetic Flux Density B of 1 T generates a force of 1 N (per-pendicular to the direction of the magnetic flux) for each 1 m of a conductor carrying a current of 1 A .(Figure.2 .4a). We.can.also.determine.the.flux.density.according.to.
eBook - PDF- M. Sibley(Author)
- 1995(Publication Date)
- Butterworth-Heinemann(Publisher)
we can define the magneticflux density as PI 8=--1' ~ 47l'r 2 with units of Wb m-2 • We cancombineEquations(3.4) and (3.5) to give B =--= !J..H (3.6) In commonwith electrostatics, the value of theconstantof proportionality this casethe permeability)is dependenton the material.Whenworking with magnetism, it is commonpracticeto work with thepermeabilityrelativeto free space. Thus, (3.7) 3,1 Some fundamental ideas 65 Magnetic flux Magnetic flux Ä## Fig, 3.1 Two separate magnetic monopoles in free space f S 4 6,ß,w where |x is the permeabilit y - a material property , (If we use the SI system of units, the force is in newton if the pole strengths are in weber (named after Wilhelm Eduard Weber , 1804-1891 , the German physicis t noted for Ms study of terrestria l magnetism), jut is in H m 1 , and r is im metre. The reason for the choice of units for jx will become dear when we conside r inductance in Section 3.11.) It is now a simple matter to introduce the idea of magneti c field strengt h in the same way that we introduced electric field strength , Thus, the force on a magneti c pole of strengt h p 2 is F = p 2 H where H is the magneti c field strengt h given by H^' (33) (3,4) 4iT|jir 2 with units of newton per weber , If we adap t Gauss ' law to magnetostatics, we can say that the magneti c lux emitted by a pole is equa l to the strengt h of the pole, Thus we can define the magneti c flux densit y as B-4irr 2 with units of Wb m. We can combine Equations (3.4) and (3.5) to give B = fiJI (3.5) (3.6) In common with electrostatics , the value of the constan t of proportionalit y (in this case the permeabilitf ) is dependen t on the materia l When working with magnetism , it is common practice to work with the permeabilit y relative to free space . Thus, §% ^ 0 (3.7) 66 Electromagnetic fields where /-La is the permeability of free space with value 41T X 10--7 H m -1. Unfortunatelytherelativepermeabilityof amagneticmaterialvariesaccording to theflux density.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
Finally, the emergent field of quantum mechanics was merged with electrodynamics to form quantum electrodynamics or QED. Definitions, units, and measurement The term magnetic field is used for two different vector fields, denoted B and H . There are many alternative names for both. The magnetic field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q , and moving in a B-field with a velocity, v , experiences a force, F , called the Lorentz force. Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole. The H -field is defined as a modification of B due to magnetic fields produced by material media. Outside of a material (i.e., in vacuum) the B and H fields are indistinguishable. (They only differ by a multiplicative constant.) Inside a material, though, they may differ in relative magnitude and even direction. Often, though, they differ only by a material dependent multiplicative constant. The B-field is measured in teslas in SI units and in gauss in cgs units. (1 tesla = 10,000 gauss). The SI unit of tesla is equivalent to (newton × second)/(coulomb × metre). The H-field is measured in ampere-turn per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. Devices used to measure the local magnetic field are called magnetometers. Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects can be determined by noting their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation which is detectable in radio waves.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
The magnetic field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q , and moving in a B-field with a velocity, v , experiences a force, F , called the Lorentz force. Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole. ________________________ WORLD TECHNOLOGIES ________________________ The H -field is defined as a modification of B due to magnetic fields produced by material media. See H and B inside and outside of magnetic materials below for the relationship between B and H . Outside of a material (i.e., in vacuum) the B and H fields are indistinguishable. (They only differ by a multiplicative constant.) Inside a material, though, they may differ in relative magnitude and even direction. Often, though, they differ only by a material dependent multiplicative constant. The B-field is measured in teslas in SI units and in gauss in cgs units. (1 tesla = 10,000 gauss). The SI unit of tesla is equivalent to (newton·second)/(coulomb·metre). The H-field is measured in ampere-turn per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. Devices used to measure the local magnetic field are called magnetometers. Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation which is detectable in radio waves. The smallest precision level for a magnetic field measurement is on the order of attoteslas (10 −18 tesla); the largest magnetic field produced in a laboratory is 2,800 T (VNIIEF in Sarov, Russia, 1998).
- John G. Webster(Author)
- 2003(Publication Date)
- CRC Press(Publisher)
The field of a bar magnet or any other magnetized object, when measured at a distance much greater than its longest dimension, is described by Equation 12.1: FIGURE 12.1 Magnetic field sensors are divided into two categories based on their field strengths and measurement range: magnetometers measure low fields and gaussmeters measure high fields. TABLE 12.1 Field Strength Instrument Characteristics Range Resolution Bandwidth Instrument (mT) (nT) (Hz) Comment Induction coil 10 –10 to 10 6 Variable 10 –1 to 10 6 Cannot measure static fields Fluxgate 10 –4 to 0.5 0.1 Dc to 2 ¥ 10 3 General-purpose vector magnetometer SQUID 10 –9 to 0.1 10 –4 Dc to 5 Highest sensitivity magnetometer Hall effect 0.1 to 3 ¥ 10 4 100 Dc to 10 8 Best for fields above 1T Magnetoresistance 10 –3 to 5 10 Dc to 10 7 Good for mid-range applications Proton precession 0.02 to 0.1 0.05 Dc to 2 General-purpose scalar magnetometer Optically pumped 0.01 to 0.1 0.005 Dc to 5 Highest resolution scalar magnetometer Magnetic Field Measurement 12 -3 (12.1) where â r is a unit vector along r, r is the distance between the magnetic field source and the measurement point, and ˘ m is called the magnetic dipole moment. The derivation of this equation can be found in many textbooks on electromagnetics. This is a very convenient equation for estimating the field produced by many magnetized objects. The strength or intensity of a magnetized object depends on the density of its volume-distributed moments. This intensity is called its magnetization M, which is defined as the moments per unit volume: (12.2) Like magnetic field, magnetization is a vector quantity. Magnetization is a material property that can arise from internal magnetic sources as well as be induced by an external magnetic field. There is a third magnetic vector ˘ B called magnetic induction or flux density. In free space, magnetic field and magnetic induction are proportional to one another by a constant factor m 0 .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Definitions, units, and measurement The term magnetic field is used for two different vector fields, denoted B and H . There are many alternative names for both. To avoid confusion, here we uses B-field and H-field for these fields, and uses magnetic field where either or both fields apply. The magnetic field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q , and moving in a B-field with a velocity, v , experiences a force, F , called the Lorentz force. Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole. ________________________ WORLD TECHNOLOGIES ________________________ The H -field is defined as a modification of B due to magnetic fields produced by material media. See H and B inside and outside of magnetic materials below for the relationship between B and H . Outside of a material (i.e., in vacuum) the B and H fields are indistinguishable. (They only differ by a multiplicative constant.) Inside a material, though, they may differ in relative magnitude and even direction. Often, though, they differ only by a material dependent multiplicative constant. The B-field is measured in teslas in SI units and in gauss in cgs units. (1 tesla = 10,000 gauss). The SI unit of tesla is equivalent to (newton·second)/(coulomb·metre). The H-field is measured in ampere-turn per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. Devices used to measure the local magnetic field are called magnetometers. Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation which is detectable in radio waves.
eBook - PDF- Rajeev Bansal(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Recording and storing various data are most commonly accomplished using y Deceased. — Milica and Zoya Popovic´ Montre ´al, Quebec Boulder, Colorado 89 magnetic storage components, such as computer disks and tapes. Most household appliances, as well as industrial plants, use motors and generators, the operation of which is based on magnetic forces. The goal of this chapter is to present: Fundamental theoretical foundations for magnetostatics, most importantly Ampere’s law Some simple and commonly encountered examples, such as calculation of the magnetic field inside a coaxial cable A few common applications, such as Hall element sensors, magnetic storage, and MRI medical imaging. 3.2. THEORETICAL BACKGROUND AND FUNDAMENTAL EQUATIONS 3.2.1. Magnetic Flux Density and Lorentz Force The electric force on a charge is described in terms of the electric field vector, E . The magnetic force on a charge moving with respect to other moving charges is described in terms of the magnetic flux density vector , B . The unit for B is a tesla (T). If a point charge Q [in coulombs (C)] is moving with a velocity v [in meters per second (m/s)], it experiences a force [in newtons (N)] equal to F ¼ Q v B ð 3 : 1 Þ where ‘‘ ’’ denotes the vector product (or cross product) of two vectors. The region of space in which a force of the form in Eq. (3.1) acts on a moving charge is said to have a magnetic field present. If in addition there is an electric field in that region, the total force on the charge (the Lorentz force) is given by F ¼ Q E þ Q v B ð 3 : 2 Þ where E is the electric field intensity in volts per meter (V/m). 3.2.2. The Biot^Savart Law The magnetic flux density is produced by current-carrying conductors or by permanent magnets. If the source of the magnetic field is the electric current in thin wire loops, i.e. current loops, situated in vacuum (or in air), we first adopt the orientation along the loop to be in the direction of the current in it.
eBook - PDF- Andrew J. Flewitt(Author)
- 2022(Publication Date)
- Wiley(Publisher)
(4.5) and (4.6) shows that J M = |M| (4.7) or in other words, the magnetization is the effective surface current whose effect would be to produce the observed magnetic dipole moment of the material. Let us assume that we have a material in which all of the microscopic magnetic dipole moments are randomly aligned when no external field is applied. Inspection of the expres- sions for the Magnetic Flux Density produced by a dipole (Eq. (4.2)) and the magnetization due to the dipoles (Eq. (4.3)) would lead us to expect that the magnetization induced is pro- portional to B/𝜇 0 . The constant of proportionality 𝜒 B is called the magnetic susceptibility, so that M = 𝜒 B B 𝜇 0 (4.8) It is analogous to the electric susceptibility (Eq. (2.9)) and is also similarly dimensionless. We now introduce a new quantity: the magnetic field H. This is analogous to the elec- tric field E, and, like the electric field, it is a measure of the actual field that will produce a real force acting on a moving charge in the presence of the field. The magnetic flux den- sity B that we have been using throughout Chapter 3 is like the electric flux density D; it is simply a mathematical construction which makes calculation of magnetic fields more straightforward. For the simple magnetic material which we have been considering where the linear rela- tion of Eq. (4.8) between magnetization and applied Magnetic Flux Density is valid, a simple linear relation also holds between B and H given by B = 𝜇 0 𝜇 r H (4.9) 54 Electromagnetism for Engineers which is analogous to the relationship between electric field and electric flux density (Eq. (2.15)). We have already defined 𝜇 0 as being the permeability of free space (see Section 3.3), while 𝜇 r is known as the relative permeability and is a material-dependent quantity. The relative permeability of free space is unity. Together, the quantity 𝜇 0 𝜇 r is known simply as permeability.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Finally, the emergent field of quantum mechanics was merged with electrodynamics to form quantum electrodynamics or QED. Definitions, units, and measurement The term magnetic field is used for two different vector fields, denoted B and H . There are many alternative names for both. The magnetic field can be defined in many equivalent ways based on the effects it has on its environment. For instance, a particle having an electric charge, q , and moving in a B-field with a velocity, v , experiences a force, F , called the Lorentz force. Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole. The H -field is defined as a modification of B due to magnetic fields produced by material media. Outside of a material (i.e., in vacuum) the B and H fields are indistinguishable. (They only differ by a multiplicative constant.) Inside a material, though, they may differ in relative magnitude and even direction. Often, though, they differ only by a material dependent multiplicative constant. The B-field is measured in teslas in SI units and in gauss in cgs units. (1 tesla = 10,000 gauss). The SI unit of tesla is equivalent to (newton × second)/(coulomb × metre). The H-field is measured in ampere-turn per metre (A/m) in SI units, and in oersteds (Oe) in cgs units. Devices used to measure the local magnetic field are called magnetometers. Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects can be determined by noting their effects on local charged particles. For instance, electrons spiraling around a field line produce syn-chrotron radiation which is detectable in radio waves.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ For linear, non-dispersive, materials (such that B = μ H where μ is frequency-independent), the energy density is: (Valid only for linear materials with negligible material dispersion) If there are no magnetic materials around then μ can be replaced by μ 0 . The above equation cannot be used for nonlinear materials, though; a more general expression given below must be used. In general, the incremental amount of work per unit volume δW needed to cause a small change of magnetic field δ B is: Once the relationship between H and B is known this equation is used to determine the work needed to reach a given magnetic state. For hysteretic materials such as fer-romagnets and superconductors the work needed will also depend on how the magnetic field is created. For linear non-dispersive materials, though, the general equation leads directly to the simpler energy density equation given above. Electromagnetism: the relationship between magnetic and electric fields Faraday's Law: Electric force due to a changing B -field A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in the coil). This is known as Faraday's law and forms the basis of many electrical generators and electric motors. Mathematically, Faraday's law is: where is the electromotive force (or EMF , the voltage generated around a closed loop) and Φ m is the magnetic flux —the product of the area times the magnetic field normal to that area. (This definition of magnetic flux is why B is often referred to as Magnetic Flux Density.) The negative sign is necessary and represents the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it. This phenomenon is known as Lenz's Law.
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