Pittsburgh, PHYS 0175
Excerpt: ... or spin) S. Associated with this spin is an intrinsic spin magnetic dipole moment S. For an electron the magnitude of S is B = eh/(4me) = 9.27x10-24 J/T which is called a Bohr magneton. In an external magnetic field Bext an electron rr B has potential energy U S g ext When an electron is bound to an atom, it has an additional angular momentum called orbital angular momentum Lorb because of its orbital motion. Associated with Lorb the electron has an orbital er r magnetic dipole moment orb Lorb 2me Both Lorb and orb are quantized, i.e. they can have only certain discrete values. When an atom is placed in an external magnetic field Bext, a potential energy U can be associated with the orientation of the orbital magnetic dipole moment of each electron in the atom. Its value is rr U orb g ext B Magnetic Materials: As we have just seen, each electron in an atom has a spin magnetic dipole moment and an orbital magnetic dipole moment which combine vectorially. The ve ...
University of Florida, PHY 2049
Excerpt: ... PHY2061 Enriched Physics 2 Lecture Notes Magnetic Dipoles Magnetic Dipoles Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. Magnetic Field of Current Loop B z R r x I y For distances R r (the loop radius), the calculation of the magnetic field does not depend on the shape of the current loop. It only depends on the current and the area (as well as R and ): 0 cos Br = 2 4 R 3 B= B = 0 sin 4 R 3 where = iA is the magnetic dipole moment of the loop Here i is the current in the loop, A is the loop area, R is the radial distance from the center of the loop, and is the polar angle from the Z-axis. The field is equivalent to that from a tiny bar magnet (a magnetic dipole). We define the magnetic dipole moment to be a vector pointin ...
University of Florida, PHY 2061
Excerpt: ... PHY2061 Enriched Physics 2 Lecture Notes Magnetic Dipoles Magnetic Dipoles Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. Magnetic Field of Current Loop z R y x r For distances R ? r (the loop radius), the calculation of the magnetic field does not depend on the shape of the current loop. It only depends on the current and the area (as well as R and ): cos Br = 2 0 4 R 3 B A = sin B = 0 4 R 3 where =i is the magnetic dipole moment of the loop Here i is the current in the loop, A is the loop area, R is the radial distance from the center of the loop, and is the polar angle from the Z-axis. The field is equivalent to that from a tiny bar magnet (a magnetic dipole). We define the magnetic dipole moment to be a vector pointing out of the plane of the current loop and with a mag ...
Rhode Island, PHYS 204
Excerpt: ... Magnetic Dipole in Uniform Magnetic Field Magnetic dipole moment : = IA^ n Torque exerted by magnetic field: = B Potential energy: U = - B Z Z ()d = B U () = - /2 sin d = -B cos /2 Note: () and d have opposite sign. . ^ = IAn ^ n I B tsl198 p.1/1 ...
UCLA, CHEM 113A
Excerpt: ... Preview #14 (Chem113A W09, due Fri. 2/6/09 at 12:05pm in class) Attendance record: I am [ ] present at or [ Assigned reading: Engel 6.1-6.2 ] absent from this class meeting (see date and time above). Name:_ Forming study groups is permissible, but you must construct your solutions independently. By writing down my name, I confirm that I strictly obey the academic ethic code when doing this preview and my statement on attendance (above) is correct. Please write down the names of everyone who you worked with on this preview in the space above. [1] Commutator. Please change the momentum to the position x. [2] Stern-Gerlach experiments. This is the Stern-Gerlach experiment corresponding exactly to Fig. 6.3 (p. 85). Please change the 3rd SG device from SG z to SG x and then predict the outcome (including probability) after the third SG device. Please clearly state your reasoning/arguments. Note: SG z means Stern-Gerlach device measuring magnetic dipole moment m Z which o ...
Loyola Chicago, LEC 112
Excerpt: ... Then: Fwire = I l B . We now consider the interaction of a loop of wire carrying a current with a uniform field B . Since the loop consists of parallel wires on either side carrying currents in the opposite direction then it is clear that the net force on the loop is zero. However, one finds in general that the is a net torque on the loop and this is given by: loop = I A B . Hence, we define the magnetic dipole moment of the loop by: Def. Magnetic Dipole Moment (of a current carrying loop): I A . Then the interaction of the loop with a magnetic field can be written: Fnet = 0 ; loop = B . Note the similarities for the interaction of an electric dipole with an electric field. Hence, the simplest magnetic structure is a dipole, or current loop. This then explains the origin of permanent magnetism. When a piece of iron is magnetized, the orbitals of electrons in the atoms are aligned with the field. Each orbiting electron acts as a tiny current loop and possesses a magnetic dipol ...
University of Florida, PHY 3101
Excerpt: ... PHY3101 Modern Physics Lecture Notes Spin 1 Angular Momentum and Spin Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. Magnetic Dipoles Consider a small current loop: z B R y r x I For distances R > r (the loop radius), the calculation of the magnetic field does not depend on the shape of the current loop. It only depends on the current and area (as well as R and ) R B = 2 I A cos v | R B=S sin | B =IA R T r 3 3 Here I is the current in the loop, A is the loop area, R is the radial distance from the center of the loop, and is the polar angle from the Z-axis. The field is equivalent to that from a tiny bar magnet (a magnetic dipole). Define the magnetic dipole moment to be a vector pointing out of the plane of the loop: v v IA D. Acosta Page 1 1/3/2001 PHY3 ...
Lehigh, PHYSIC 2
Excerpt: ... Lecture-18 Lectures thus far covered: Electrostatics in vacuum and with dielectrics Magnetic fields due to electric current: a line current, a long solenoid, a toroid, a fat wire and a coaxial cable. Magnetic Field is non-conservative r r B dl = o I enclosed = o I i i Induced electric field due to changing B-flux Induced magnetic field due to changing E-flux Steady magnetic fields in vacuum: What happens if in material medium? Materials in Magnetic Field Experimental Fact: If an iron core is placed within a solenoid, the magnetic field becomes MUCH stronger. Different kinds of magnetic materials: Ferromagnetic; Paramagnetic; and Diamagnetic 1 Atomistic Origin of Magnetism Electron spin An electron has intrinsic spin r angular momentum S and associated spin magnetic dipole r moment , where s e r s = - S m r Note that S is quantum mechanical quantity. r Electron orbital magnetic dipole moment An orbiting electron inside an atom has orbital angular momentum Lorb and associ ...
East Los Angeles College, PHY 331
Excerpt: ... PHY331 Magnetism Lecture 3 Last week. Derived magnetic dipole moment of a circulating electron. Discussed motion of a magnetic dipole in a constant magnetic field. Showed that it precesses with a frequency called the Larmor precessional frequency 1 This week. Discuss Langevin's theory of diamagnetism. Use angular momentum of precessing electron in magnetic field to derive the magnetization of a sample and thus diamagnetic susceptibility. Will set the scene for the calculation of paramagnetic susceptibility. Langevin's theory of diamagnetism We want to calculate the sample magnetisation M and the diamagnetic susceptibility (recall M = H) Every circulating electron on every atom has a magnetic dipole moment The sum of the magnetic dipole moment s on any atom is zero (equal numbers circulating clockwise and anticlockwise ?) The magnetisation M arises from the reaction to the torque due to the applied magnetic field B which creates the Lamor L precessional motion. 2 i) the angul ...
Wisconsin, PHYS 208
Excerpt: ... iew: Electric Dipole Moments Electric dipole moment p. -q - d + +q p= qd B 4 I I I 3 b 1 a F4 b I 2 A x IA: magnetic dipole moment B F = 0 = pE r U = -p E 4 bsin top view F2 A : Area Vector 3 face view 1 Magnetic Dipole Moment s N Quick Quiz 1 B A magnetic dipole moment initially points at 45o. When a uniform horizontal B field is applied, which of the followings will happen? 1. No change Magnetic dipole moment . S Macroscopic =IA Microscopic L angular momentum of orbiting or spin F = 0 rv = B r U = - B in B Field 5 B 2. Points towards the B field 3. Points against the B field 4. Points normal to the B field B B B definition of magnetic moment 6 Quick Quiz 2 A magnetic dipole moment initially points at 135o. When a uniform horizontal B field is applied, which of the followings will happen? 1. No change Side Story (Chapter 8): Stable and Unstable Equilibrium B B B 2. Points towards the B ...
Wisconsin, PHYS 202
Excerpt: ... the direction of the force on each side? (Lecture 11 review: FB= ILxB ) FB=0 4 Torque on a Current Loop In Uniform B Field Exercise: For a current loop in a uniform B field, show that the torque on the loop is: |=IABsin (Quiz: In what direction?) r r r Conveniently, the result can be rewritten as: = IA B . 1 FB I I I 3 . . . . . . . . . I. . .1 . . . . . . . . 4 B X I 2 . .F. . . . . . . . . . . . . .F.B . . . B B I I 4 I I I 3 b 1 F4 a . . . . . . . . . . . . .2. . . . . . . . 3 . . Case 2 recall:FB=0 FB . I I 2 A x IA: magnetic dipole moment B F2 FB=0 bsin top view A : Area Vector Case 1 face view Magnetic Dipole Moment s N Magnetic dipole moment . S B Electric dipole moment p. + Review and Compare: Electric Dipole Moments +q -q - p= qd Macroscopic =IA IA F = 0 = B r U = - B in B Field r v Microscopic L angular momentum of orbiting or spin F = 0 = pE ...
Wisconsin, PHYS 208
Excerpt: ... 4 I I I 3 b 1 a F4 b I 2 A x IA: magnetic dipole moment B F2 bsin top view A : Area Vector 3 face view Review: Electric Dipole Moments Electric dipole moment p. -q - d + +q p= qd F = 0 = pE U = -p E 4 r Magnetic Dipole Moment s N Magnetic dipole moment . S B Macroscopic =IA F = 0 = B r U = - B in B Field r v Microscopic L angular momentum of orbiting or spin definition of magnetic moment 5 Quick Quiz 1 A magnetic dipole moment initially points at When a uniform horizontal B field is applied, which of the followings will happen? 1. No change 45o. B 2. Points towards the B field 3. Points against the B field 4. Points normal to the B field B B B 6 Quick Quiz 2 A magnetic dipole moment initially points at When a uniform horizontal B field is applied, which of the followings will happen? 1. No change 135o. B 2. Points towards the B field 3. Points against the B field 4. Points normal to the ...
Mesa State, PHYS 321
Excerpt: ... ow that the probability with which the particle emerges x from the last Stern-Gerlach apparatus is 1/4. If the particle does emerge from the last Stern-Gerlach apparatus, determine its state. These questions can only be answered using the framework for dealing with measurements outcomes and probabilities provided that between successive measurements the particle is subject to no outside influences that could alter its state. The subject of dynamics deals with describing the evolution of the state of a spin-1/2 particle in situations where outside influences will change its state. 4.1 Evolution of classical magnetic dipoles. A magnetic field B will exerte a torque on classical magnetic dipole with dipole moment. The torque is given by =B (II.4.2) where is the magnetic dipole moment of the particle. The torque determine the change in the spin angular momentum via dS = . (II.4.3) dt 73 Eqs. (II.1.6) and (II.4.2) then imply that for a particle of mass, M and charge Q, d gQ = B dt 2M (II.4.4) The im ...
Colorado State, ECE 505
Excerpt: ... EE 505 Nanostructures: Fundamentals and Applications Spring 2009 Prof. Carmen S. Menoni Homework #1 Due Date: February 19, 2009 * 1. Explain which are the similarities and dissimilarities between electrons in a crystal and an electromagnetic field propagating in free space. 2. The ionization energy of the hydrogen atom in its ground state is Eion=13.6 eV. Calculate the frequency and wavelength of the electromagnetic radiation that just ionize the atom. 3. The magnetic dipole moment of a current loop is defined by = I A , where I is the current and A is the area of the loop. A current loop may be represented by a charge e rotating at constant speed in a small circular orbit. 4. Use classical reasoning to show that the magnetic dipole moment of the loop is related to L the orbital angular momentum of the particle by e = L 2m where m is the mass of the particle. If the magnitude of L is h = h 2 , calculate the magnitude of for (i) and el ...
LSU, PHYS 21022
Excerpt: ... Physics 2102 Aurora Borealis Jonathan Dowling Lecture 20: WED 04 MAR Magnetic fields Ch.28.9-10 "I'll be back. Torque on a Current Loop: Rectangular coil: A=ab, current = i Principle behind electric motors. Net force on current loop = 0 But: Net torque is NOT zero! F1 = F3 = iaB F" = F1 sin(! ) Torque = " = F#b = iabB sin(! ) For a coil with N turns, = N I A B sin, where A is the area of coil Magnetic Dipole Moment We just showed: = NiABsin N = number of turns in coil A=area of coil. Define: magnetic dipole moment ! ^ = ( NiA)n ! ^ , n Right hand rule: curl fingers in direction of current; thumb points along ! ! ! " = !B As in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field. Electric vs. Magnetic Dipoles +Q p=Qa -Q QE ! ^ = ( NiA)n ! ! ! "E = p # E ! ! UE = " p # E QE ! ! ! " B = # B! ! U B = " # B ...