3.7.5 Magnetic Fields

3.7.5 Magnetic Fields

1. Magnetic Flux Density

   • Symbol B, unit Tesla (T)
     • Force per unit length per unit current
   • Force on current carrying wire, F=BIl
     • I - current, l - length of wire in magnetic field
     • when field is perp to current
   • Fleming's left hand rule
     • all fingers perp

2. Moving Charges in a Magnetic Field

   • F=BQv
     • Q - charge, v - velocity
     • no force if stationary or moving parallel to field
     • Force proportional to B, Q, v
   • current in positive direction
     • remember when using electrons to reverse direction
   • Applications
     • from circular motion -> F=mvv/r
       • BQv=mvv/r
         • BQ=mv/r
           • r decreases if
             • B or v increase
             • specific charge increases
     • Cyclotron
       • 2 "dees"
         • magnetic field in dees curves the particles' paths
           • Each time gap is crossed, velocity increases so radius increases
             • when r = r of dee, particle is ejected
       • source of charged particles at centre
       • alternating current induces alternating electric field which accelerates the particles in a straight line across the gap between the dees
         • alternates with perfect time period for time for particle to move edge back to edge
     • Mass spectrometer
       • If v not perfect through velocity selector, deflected to + or - plate so don't reach vacuum
         • perfect v -> magnetic field force cancelled out by electric field force
       • greater specific charge -> smaller radius

3. Magnetic Flux and Flux Linkage

   • Magnetic flux, Φ=BA
     • unit - Weber (Wb)
   • Flux linkage, NΦ=BANcosθ
     • unit - Weber turns (Wb turns)
   • rectangular coil

4. Electromagnetic Induction

   • Faraday's Law
     • induced emf in a circuit is equal to the rate of change of flux linkage through the circuit
       • induced emf = -NΔΦ/Δt
         • negative as induced emf acts in opposite direction as to what causes it (Lenz's Law)
   • Lenz's Law
     • direction of induced current is always such as to oppose the change causing it
       • otherwise energy would be created
   • Examples

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