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Magnetic Forces, Materials and Devices INEL 4151 ch 8 Dr. Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPRM magnetic-batteries.php

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Applications Motors Transformers MRI More… 65w

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Forces due to Magnetic fields B= H= magnetic field density H=magnetic field intensity Force can be due to: B on moving charge, Q B on current 2 currents B is defined as force per unit current element

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Forces on a Charge Analogous to the electric force: We have magnetic force: If the charge moving has a mass m, then: The total force is given by: Note that F m is perpendicular to both u and B Usually F m < F e

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Forces on a current element The current element can be expressed as: So we can write: For closed path Line I =[A] current element Surface K=[A/m] current element Volume J=[A/m 2 ] current element

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Force between two current elements Each element produces a field B, which exerts a force on the other element. I1I1 I2I2 R 21

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P.E. 8.4 Find the force experienced by the loop if I 1 =10A, I 2 =5A, o =20cm, a=1cm, b=30cm I1I1 I2I2 a b z F1F1 F2F2 F3F3 F4F4 z Divide loop into 4 segments.

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Since I 1 is infinite long wire: F1F1 I1I1 I2I2 a b z For segment #1, Force #1

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F2F2 I1I1 I2I2 a b z For segment #2, The B field at segment #2 due to current 1.

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The field at segment 3: F3F3 I1I1 I2I2 a b z For segment #3, Force #3

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F4F4 I1I1 I2I2 a b z For segment #4, The B field at segment #4 due to current 1.

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The total force en the loop is The sum of all four: Note that 2 terms cancel out: F1F1 F2F2 F3F3 F4F4 z I 1 =10A, I 2 =5A, o =20cm, a=1cm, b=30cm Attracts!

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Magnetic Torque and Moment The torque in [N m]is: Where m is the magnetic dipole moment: Where S is the area of the loop and a n is its unit normal. This applies if B is uniform Inside a motor/generator we have many loops with currents, and the Magnetic fields from a magnet exert a torque on them. B z SIDE VIEW B

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Torque on a Current Loop in a Magnetic Field CD Motor

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Magnetic Torque and Moment The torque in [N m]is: The Magnetic torque can also be expressed as:

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Magnetization (similar to Polarization for E) Atoms have e- orbiting and spinning – Each have a magnetic dipole associated to it Most materials have random orientation of their magnetic dipoles if NO external B-field is applied. When a B field is applied, they try to align in the same direction. The total magnetization [A/m]

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Magnetization The magnetization current density [A/m 2 ] The total magnetic density is: Magnetic susceptibility is: The relative permeability is: Permeability is in [H/m].

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Classification of Materials according to magnetism Magnetic r ≠1 Non-magnetic r =1 Ex. air, free space, most materials in their natural state. Diamagnetic r ≤1 Electronic motions of spin and orbit cancel out. lead, copper, Si, diamonds, superconductors ( r =B=0). Are weakly affected by B Fields. Paramagnetic r ≥1 (air, platinum, tungsten, platinum ) Temperature dependent. Not many uses except in masers Ferromagnetic r >>1 Iron, Ni,Co, steel, alloys Loose properties if heated above Curie T (770C) Nonlinear: r varies

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B-H or Magnetization curve When an H-field is applied to ferromagnetic material, it’s B increases until saturation. But when H is decreased, B doesn’t follow the same curve.

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Hysteresis Loop Some ferrites, have almost rectangular B-H curves, ideal for digital computers for storing information. The area of the loop gives the energy loss per volume during one cycle in the form of heat. Tall-narrow loops are desirable for electric generators, motors, transformers to minimize the hysteresis losses.

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Magnetic B.C. We’ll use Gauss Law & Ampere’s Circuit law

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B.C.: Two magnetic media Consider the figure below: B1B1 B2B2 B 1t B 1n B 2t B 2n hh S 22 11

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B.C.: Two magnetic media Consider the figure below: H1H1 H2H2 H 1t H 1n H 2t H 2n ab c d w hh 11 22 11 K

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P.E. 8.8 Find B 2 Region 1 described by 3x+4y ≥10, is free space Region 2 described by 3x+4y ≤10 is magnetic material with r =10 Assume boundary is current free. OJO: Error en Solucionario!

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P.E. 8.7 B-field in a magnetic material. In a region with r =4.6 Find H and susceptability A/m

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How to make traffic light go Green when driving a bike or motorcycle Stop directly on top of induction loop on the street Attach neodymium magnets to the vehicle Move on top of loop Push crossing button Video detectors er-Green-Traffic-Lights er-Green-Traffic-Lights n/loops.html n/loops.html

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Inductors If flux passes thru N turns, the total Flux Linkage is This is proportional to the current I So we can define the inductance as: then:

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Units of Inductance

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When more than 1 inductor *Don’t confuse the Magnetization vector, M, with the mutual inductance!

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Self -inductance The total energy in the magnetic field is the sum of the energies: The positive is taken if currents I 1 and I 2 flow such that the magnetic fields of the two circuits strengthen each other. See table 8.3 in textbook with formulas for inductance of common elements like coaxial cable, two-wire line, etc.

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P.E solenoid A long solenoid with 2 x 2 cm cross section has iron core (permeability is 1000x ) and 4000 turns per meter. If carries current of 0.5A, find: Self inductance per meter Note L is Independent of current

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Magnetic Circuits Magnetomotive force Reluctance Like V=IR Ex: magnetic relays, motors, generators, transformers, toroids Table 8.4 presents analogy between magnetic and electric circuits In units of ampere-turns

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Magnetic Circuits

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Ex. Find current in coil needed to produced flux density of 1.5T in air gap. Assume r =50 and all cross sectional area is 10 cm 2

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8.42 A cobalt ring ( r =600) has mean radius of 30cm. If a coil wound on the ring carries 12A, calculate the N required to establish an average magnetic flux density of 1.5 Teslas in the ring. radius of 30cm

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Force on Magnetic materials Relay N turns, current I B.C. B 1n =B 2n (ignore fringing) Total energy change is used to displace bar a distance dl. S=cross sectional area of core

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P.E U-shape electromagnet Will lift 400kg of mass(including keeper + weight) Iron yoke has r =3,000 Cross section =40cm 2 Air gap are 0.1mm long Length of iron=50cm Current is 1A Find number of turns, N Find force across one air gap Esto nos da el B en el air gap.

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MagLev magnetic Levitation Use diamagnetic materials, which repel and are repelled by strong H fields. Superconductors are diamagnetic. Floating one magnet over another Maglev train 312 mph Regular train 187 mph

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