A charge particle in a cyclotron,what effect on radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?
Asked by Anushass2911
21st September 2018,
8:37 AM
Answered by Expert
Answer:
A moving charge in a cyclotron will move in a circular path under the influence of a constant magnetic field.
If the time to complete one orbit of radius R is T, which is given by, T = 2πR/v ...............(1)
where v is linear speed of the charge q.
If the charge q is moving in magnetic field B with linear speed v, then we have, q×B×v = m×v2/R ...........(2)
m is mass of the charge.
eqn.(2) can be simplified as, R/v = m/(qB) ....................(3)
from (1) and (3), we write T = 2π×m / (q×B) ...............(4)
Hence the period is independent of radius. If a varying voltage in the form of square wave is appled at angular frequecy qB/m between the two semi-circular discs ( called as 'dees') of cyclotron which are placed in the magnetic field, the charge will spiral outward by increasing its speed v and corresponding increase in orbit radius R so that the ratio R/v is constant.
The applied varying voltage of angular frequency ω = qB/m between the two 'dees' of the magnetic field region, helps to boost the charge at just the right time to accelerate it across the gap of 'dees'. If the frequency is doubled, the charge will be accelerated at alternate cycles and there will not be change in orbit radius.
Answered by Expert
21st September 2018,
12:08 PM
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