Concept explainers
(a) To Determine:
The magnetic field (B).
Answer to Problem 10P
Solution:
The magnetic field (B)is
Explanation of Solution
Given Info:
The radius of cyclotron is 1.0m.
The energy is 12 MeV or .
Formula Used:
Cyclotron is based on the principle that a charged particle can be accelerated to a very high energy with a small alternate electric field and with the help of a magnetic field.
Magnetic force=
(I)
• ‘q’ is the charge of deuteron
• ‘B’ is magnetic field
• ‘v’ is velocity of particle
• ’m’ is mass of the particle
• ‘r’ is the radius of particle
The kinetic energy of the charge particle is,
Substitute ‘v’ from equation (I)in the kinetic energy
The formula is used to find magnetic field,
Calculation:
Substitute for ‘E’ and 1.0m for ‘r’ to find ‘B’
(II)
Thus, the magnetic field is
(b) To Determine:
The frequency (f).
Answer to Problem 10P
Solution:
The frequency (f)is
Explanation of Solution
Given Info:
The radius of cyclotron is 1.0m.
The energy is 12 MeV or.
Formula Used:
The period (T)is defined as,
• ’T’ is period of revolution.
• ‘m’ is the mass of particle.
Calculation:
Substitute 0.708 T for ‘B’ from equation (II)to find ‘f’
(III)
Thus, the frequency is .
(c) To Determine:
The number of revolution (n)
Answer to Problem 10P
Solution:
The number of revolution is .
Explanation of Solution
Given Info:
The radius of cyclotron is 1.0m.
The energy is 12 MeV or.
The potential difference is 22V or
Formula Used:
• ’n’ is number of revolution.
• ‘V’ is the potential difference.
Calculation:
Substitute for ‘E’ and for ‘V’ to find ‘n’,
(IV)
Thus, the number of revolution is .
(d) To Determine:
The time taken to exit (t).
Answer to Problem 10P
Solution:
The time taken to exit (t)is .
Explanation of Solution
Given Info:
The radius of cyclotron is 1.0m.
The energy is 12 MeV or.
The potential difference is 22V or
Formula Used:
• ’t’ is time to exit.
• ‘n’ is number of revolution.
• ‘f’ s frequency of revolution
Calculation:
Substitute equation (III0 and (IV)to find ‘t’,
.
(V)
Thus, the time it takes to exit is
(e) To Determine:
The distance (d)travel during time ’t’.
Answer to Problem 10P
Solution:
The distance travel (d)during time ‘t’ is .
Explanation of Solution
Given Info:
The radius of cyclotron is 1.0m.
The energy is 12 MeV or.
The potential difference is 22V or
Formula Used:
The formula used to find distance is,
• ’d’ is distance.
• ‘n’ is number of revolution.
• ‘r’ is radius.
Calculation:
Substitute 273 rev for ‘n’ and 1.0 m for ‘’ to find ‘d’,
(VI):
Thus, distance travel during time ‘t’ is
Chapter 32 Solutions
Physics: Principles with Applications
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