Magnetic Fields

Magnetic Fields

1. Current- carrying wire

   • Mag field is produced around the material in concentric circles.
   • Right Hand Rule- right thumb points in direction of conventional current, curled fingers point in direction of mag field lines
     • Conventional current: goes from +ve to -ve. Opposite to the flow of electrons as they go from -ve to +ve

2. F=BIL

   • Current-carrying wire placed in external mag field, field around wire and field from magnets add together.
     • Resultant field- field lines closer together- stronger field- bunched lines cause force on wire
   • Direction of movement of force, perpendicular to both, magnetic field lines and direction of (conventional) current
     • Fleming's Left-hand rule
   • Motor effect: coil of wire that is free to rotate between two opposite magnetic poles. When current flows through coil, it experiences motor effect. The direction of the current must be reversed every half turn.
     • Force on the wire can be altered by altering voltage, current or Strength of field
   • F∝B
     • Force is at right angles to field lines.
     • Magnetic flux density, B: Force on one meter of a current-carrying coil, with a current of 1 amp, at right angles to the field lines.
       • Flux density: vector quantity. Has direction and magnitude.
   • F∝L
     • When the direction of the current is at 90 degrees to the magnetic field lines, size of current ∝ force
       • Force is greatest when wire is 90 degrees to field. Force is 0 when wire is parallel to field
   • 1T= number of flux lines measured in Webers, per unit area.

3. Forces on Charged particles

   • F=BQV
     • Electic current--> flow of charge I
       • I=Q/t
     • Charged particle that moves a distance L in time t has velocity v=L/t ----> L=vt
       • Velocity is perpendicular to the direction of the magnetic field.
     • Independent of particles mass
   • Deflection
     • Deflected via circular path.
       • Fleming's left hand rule says, a force on a moving charge is perpendicular to its direction of movement
         • Condition for circular motion
         • FLHR for charged particles- use second finger (current) for +vely charge
           • Reverse direction of second finger if using FLHR for -vely charged particle
     • F=ma---> a=v^2/r---> F=mv^2/r ---> centripetal force is dependent on particles mass
       • F=BQv and F=mv^2/r are equal to each other
       • BQv=mv^2/r
         • BQ=mv/r
           • r=(mv)/BQ
             • radius of curvature will increase (deflected less) if B or charge on particle decreases, or if v or V increases.
             • radius of curvature will decrease (deflected more) if v decreases, or if B or charge on particle increases

4. Cyclotrons

   • Circular deflections is used in Particle accelerators
   • used in medicine i.e. making radioactive tracers or high energy beams of radiation used in radiotherapy.
   • Made from two hollow semi circular electrodes. Uniform mag is applied perpendicular to the plane of the electrodes.
     • Alternating Pd is applied between the electrodes. This accelerates them into the next electrode, with a slightly higher velocity, so radius of curvature increases. Pd reverses so that particle is accelerated again before entering the next electrode. Eventually spirals outwards and leaves the electrode.
       • Particle leaves electrode with speed v= (BQR)/m
         • Where R is the radius of the electrode
       • Particles leave electrode when the radius of their curvature is equal to the radius of the electrode
       • Time t, for particle to complete 1 full cycle of AV equal to t for particle to complete 1 full circle.
         • Distance traveled by particle, D= 2πR----> v= (BQR)/m ---> Time, T= D/V ---> 2πR/(BQR)/m ---> 2πR*m/(BQR)
           • T= 2πm/BQ
             • f=1/T
               • Frequency of alternating voltage, f= BQ/2πm
   • Charged particle is fired into one of the electrodes. Mag field makes them follow a circular path.

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