# b fields

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• Created by: Anwen
• Created on: 22-05-14 22:35
• B-fields
• Magnetic field lines
• always move N -> S
• When two oppose there is a neutral point usually denoted by X
• Flemming L.H.R
• thumb=Motion First=Field second=Current
• Flux Linkage = If the coil in the magnetic flux consists of N turns the flux linkage is given by [email protected] (@=thi) unit=WB(webber)
• F=BIlsinO
• Force on a straight wire carrying a current. If a current I flows in a length l of a wire at right angles to a magnetic field of flux density B(it's magnetic field strength)
• F=BIl     B=F/Il
• Flux density = the distance between two lines of the field (shorter distance greater density)
• Equations used to calculate flux density
• B=       (UoI)    ________   2(pie)a
• Mgnetic Flux = BAsinO unit=webber D= if a single turn coil of wire encloses an area A and a magnetic Field B makes an angle O with the normal to the plane of the coil, the magnetic flux through the coil is given by @=ABcosO or  @=ABsinO
• Relative permeability Ur = B/Bo usually from 1->300 for ferromagnetic material Ur is large and positive
• The Ampere
• To derive an expression for the force, two long straight parallel conductors at a distance 'a' apart in air carrying current I1 and I2 respectively as shown in the diagram -------->
• B1=                  (Uo*I*1) _____________    2*(pie)*a
• F=B1*I2*L
• F=    Uo*I1*I2*l ______________ 2*(pie)*a
• Wire 1 exerts a force on wire 2 and wire 2 exerts an equal and opposite force on wire 1
• I1=I2=1A l=a=1m    subin F= Uo*I1*I2*l ___________ 2*(pie)*a
• Uo  =               4(pie)x10-7       Hm^-1
• D= the ampere is that current which when flowing through 2 infinite thin wires one metre apart in vacuum produces a force between the wires of exactly 2x10-7N per m of length (A)
• Force in a changing magnetic field
• V=L/t
• I=nq/t
• t=L/v
• I=nqv/L
• F=BIL         =B{nq/L}*L =Bnqv singlecharge = F=Bqv Forelectrons = F=Bev
• How to increase the field strength within a solenoid
• filling the core with a ferrous metal e.g iron cobalt and nickel
• B=UrUonI
• The magnetic field outside the solenoid and the self inductance of the solenoid are increased in the same proportion.
• Hall Voltage
• DWhen a magnetic field B is applied to a conductor carrying current I at right angles to the field direction a so-called Hall volatage appears across the specimen at right angles to the B and I directions (L.H.R.)
• Vh.prop.B  Vh=BI/nxq
• B=magnetic field strength I=cuurent n=numberof charge carryers
• Vh =Bvd d=distance between bottom and top.
• The electrons move into the hall probe, and move in the opposite direction to thwe motion ~(LHR)~ when bottom layer is fullyaturated the electrons pass straight through the probe un deflected
• Cyclotrons, Synchrotrons and Linear accelerators
• Cyclotron
• The charged particles are accelerated in a circular path where the magnetic field is constant. Whilst the radius of the curved path changes (in a swirly pattern) the particles are accelerated by applying a PD across the gap.
• Synchrotrons
• The charged particles are also accelerated in a circular path. However the radius of the path followed by the particle remains constant whilst the applied magnetic field changes.
• Most of the worlds famous particle accelerators e.g CERN in switzerland use the synchrotron technique they reach about 99% the speed of light.
• Advantages = It's possible to accelerate the particles to higher speeds. Higher energy means more energy and smaller waves and therefore the discovery of v. small particles e.g quarks
• Disadvantages it's not possible to accelerate a continuous stream of particles. The particles are accelerated in small bunches then clear the machine before inserting the next bunch. (short burst of particles)
• Advantages = It's possible to accelerate the particles to higher speeds. Higher energy means more energy and smaller waves and therefore the discovery of v. small particles e.g quarks
• Disadvantages it's not possible to accelerate a continuous stream of particles. The particles are accelerated in small bunches then clear the machine before inserting the next bunch. (short burst of particles)
• Linear accelerators
• The future lies in the linear accelerators which accelerate particles in a straight line. The advantage being that they need less energy to operate because the particle don't expierience centripedal force / accleleration
• Centrapedal Force +acceleration
• F=            mv^2    __________ r
• F=Bqv
• F=ma
• a=w^2r
• v=rw
• v^2=w^2r^2
• a=               v^2/r
• Bqv= mv^2/r
• Bq = mv/r
• for electrons Be=mv/r
• Force between two wires carrying current
• current in the same direction attract each other (pushed together by a stronger outer field)
• If currents are in opposite direction then the wires repel each other (the strong central magnetic field pushes the wires apart)
• Deflection of charged particles
• Beta goes toward the positive in an electric field and alpha moves towards the negative(muchslower wvelocity than beta)
• Ina magnetic field the alpha particle moves up