Magnetic Fields Flashcards
define magnetic flux density
force per unit current per unit length on a wire placed at 90’ to the direction of the magnetic field
describe how a cyclotron works
- consists of two hollow dees
- alternating electric field maintained across gap by an alternating pd
- constant uniform magnetic field acts through whole accelerator
- charged particles injected into cyclotron centre where they follow a circular path due to magnetic field
- each time particle crosses gap between dees, it is accelerated + spirals out as r~v
- when radius of path=radius of dees particles exit cyclotron
why must an alternating potential difference be applied across gap between dees?
- as positively charged particle approaches gap, direction of electric field needs to equal direction of moving charge to accelerate it
- as it approaches other side of circle it needs to re-cross gap but as now travelling opposite direction, electric field must be reversed to accelerate particle
- reversal of electric field achieved by reversal of polarity
how can frequency of alternating potential difference required to accelerate particles be calculated?
- t = pi*r /v (time to travel one dee)
- BQv = mv^2 /r…. v/r = BQ/m
- t = pi*m/BQ
- T = 2pi*m/BQ (time to travel round both dees)
- f = BQ / 2pi*m
what are the limitations of cyclotrons?
spiral path of particles synched with frequency that pd alternating at + as mass of particle increases as it closer to speed of light, and frequency depends on mass, approach of particle to dee becomes out of phase with alternating pd so particle doesn’t
therefore particle can only accelerate to a few percent of speed of light
how do you calculate the number of times charged particle would have to pass between dees to reach required energy?
and time taken to reach this energy
energy in eV / alternating pd
1/T * (number of times pass between dees / 2)
define magnetic flux
the number of magnetic field lines passing through a closed surface
