26. Attraction: Power and Field.

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2. Themes. The Magnetic Field and ForceThe Hall EffectMotion of Charged ParticlesOrigin of the Magnetic FieldLaws for MagnetismMagnetic DipolesMagnetism. 3. Presentation. An electric field is an unsettling influence in space causedby electric charge. An attractive field is adisturbance in space created by moving electric charge. An electric field makes a power on electric charges. An attractive field makes a f
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26. Attraction: Force & Field

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Topics The Magnetic Field and Force The Hall Effect Motion of Charged Particles Origin of the Magnetic Field Laws for Magnetism Magnetic Dipoles Magnetism

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Introduction An electric field is an aggravation in space brought on by electric charge. An attractive field is an unsettling influence in space brought on by moving electric charge. An electric field makes a power on electric charges. An attractive field makes a power on moving electric charges.

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Magnetic Field and Force It has been found that the attractive power relies on upon the point between the speed of the electric charge and the attractive field

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Magnetic Field and Force The power on a moving charge can be composed as where B speaks to the attractive field

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Magnetic Field and Force The SI unit of attractive field is the tesla (T) = 1 N/(A.m). In any case, regularly we utilize a littler unit: the gauss (G) 1 G = 10 - 4 T

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The Hall Effect

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h The Hall Effect Consider an attractive field into the page and a present spilling out of left to right. Free positive charges will be redirected upwards and free negative charges downwards.

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h The Hall Effect Eventually, the incited electric power adjusts the attractive power: Hall Voltage t is the thickness Hall coefficient

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Motion of Charged Particles in a Magnetic Field

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Motion of Charged Particles in a Magnetic Field The attractive power on a point charge does no work . Why? The power just alters the course of movement of the point charge.

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Motion of Charged Particles in a Magnetic Field Newton\'s 2 nd Law So sweep of circle is

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Motion of Charged Particles in a Magnetic Field Since, the cyclotron time frame is Its converse is the cyclotron recurrence

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The Van Allen Belts

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Wikimedia Commons

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Origin of the Magnetic Field

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The Biot-Savart Law A point charge creates an electric field. At the point when the charge moves it creates an attractive field, B : m 0 is the attractive consistent : As drawn, the field is into the page

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The Biot-Savart Law When the expression for B is stretched out to a present component, IdL , we get the Biot-Savart law : The aggregate field is found by mix:

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P Biot-Savart Law: Example The attractive field because of a vastly long current can be processed from the Biot-Savart law: x

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Biot-Savart Law: Example Note: if your right-hand thumb focuses toward the current, your fingers will twist toward the subsequent attractive field I

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Laws of Magnetism

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Magnetic Flux Just as we accomplished for electric fields, we can characterize a flux for an attractive field: But there is a significant contrast between the two sorts of flux…

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Gauss\' Law for Magnetism Isolated positive and negative electric charges exist. Nonetheless, nobody has ever found a disconnected attractive north or south post, that is, nobody has ever found an attractive monopole Consequently, for any shut surface the attractive flux into the surface is precisely equivalent to the flux out of the shut surface

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Gauss\' Law for Magnetism This yields Gauss\' law for attraction Unfortunately, notwithstanding, in light of the fact that this law does not relate the attractive field to its source it is not helpful for registering attractive fields. Be that as it may, there is a law that is…

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I Ampere\'s Law If one wholes the dab item around a shut circle that surrounds an enduring current I then Ampere\'s law holds: That law can be used to figure attractive fields, given an issue of adequate symmetry

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z y x Ampere\'s Law: Example What\'s the attractive field a separation z over a vast current sheet of current thickness l per unit length in the y course? From symmetry, the attractive field must point in the positive y bearing above the sheet and in the negative y heading below the sheet.

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z y x Ampere\'s Law: Example Ampere\'s law expresses that the line essential of the attractive field along any shut circle is equivalent to m 0 times the present it surrounds: Draw a rectangular circle of stature 2a in z and length b in y , symmetrically put about the present sheet.

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z y x Ampere\'s Law: Example The main commitment to the basic is from the upper and lower sections of the circle. From symmetry the size of the attractive field is steady and the same on both sections. Consequently, the indispensable is only 2Bb . The enclosed current is I = l b. Along these lines, Ampere\'s law gives 2Bb = m 0 l b and therefore B = m 0 l/2

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Magnetic Force on a Current

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Magnetic Force on a Current Force on every charge: Force on wire portion: n = number of charges per unit volume

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Magnetic Force on a Current Note the heading of the power on the wire For a present component IdL the power is

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Magnetic Force Between Conductors Since the power on a current-conveying wire in an attractive field is two parallel wires, with streams I 1 and I 2 apply an attractive power on each other. The power on wire 2 is: d

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Magnetic Dipoles

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Magnetic Moment A present circle encounters no net power in a uniform attractive field. However, it does experience a F torque B The power is F = Ia B F

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Magnetic Moment Magnitude of torque where A = stomach muscle For a circle with N turns, the torque is

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Magnetic Moment It is valuable to characterize another vector amount called the attractive dipole minute then we can compose the torque as

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Example: Tilting a Loop

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Example: Tilting a Loop

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Magnetic Moment The attractive torque that causes the dipole to pivot does work and tends to diminish the potential vitality of the attractive dipole If we consent to set the potential vitality to zero at 90 o then the potential vitality is given by

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Magnetization Atoms have attractive dipole minutes because of orbital movement of the electrons attractive snapshot of the electron When the attractive minutes adjust we say that the material is polarized.

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Types of Materials display three sorts of attraction: paramagnetic diamagnetic ferromagnetic

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Paramagnetism Paramagnetic materials have perpetual attractive minutes haphazardly situated at ordinary temperatures adds a little extra field to connected attractive field

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Paramagnetism Small impact (changes B by just 0.01%) Example materials Oxygen, aluminum, tungsten, platinum

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Diamagnetism Diamagnetic materials no lasting attractive minutes attractive minutes actuated by connected attractive field B connected field makes attractive minutes contradicted to the field

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Diamagnetism Common to all materials. Connected B field prompts an attractive field inverse the connected field, in this way debilitating the general attractive field But the impact is little: B m ≈ - 10 - 4 B application

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Diamagnetism Example materials high temperature superconductors copper silver

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Ferromagnetism Ferromagnetic materials have changeless attractive minutes adjust at typical temperatures when an outer field is connected and unequivocally upgrades connected attractive field

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Ferromagnetism Ferromagnetic materials (e.g. Fe, Ni, Co, amalgams) have areas of haphazardly adjusted polarization (because of solid connection of attractive snapshots of neighboring iotas)

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Ferromagnetism Applying an attractive field causes spaces adjusted to the connected field to develop to the detriment of others that psychologist Saturation charge is achieved when the adjusted areas have supplanted all others

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Ferromagnetism In ferromagnets, some charge will stay after the connected field is diminished to zero, yielding perpetual magnets Such materials display hysteresis

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Summary Magnetic Force Perpendicular to speed and field Does no work Changes course of movement of charged molecule Motion of Point Charge Helical way about field

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Summary Magnetic Dipole Moment A present circle encounters no net attractive power in a uniform field But it experiences a torque

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Summary The attraction of materials is because of the attractive dipole snapshots of particles, which emerge from: the orbital movement of electrons and the characteristic attractive snapshot of every electron

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Summary Three classes of materials Diamagnetic M = – const • B ext , small impact (10 - 4 ) Paramagnetic M = + const • B ext little impact (10 - 2 ) Ferromagnetic M ≠ const • B ext expansive impact (1000)

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