A deuteron has the same charge as a proton but approximately twice the proton mass.Suppose deuterons are being accelerated in a cyclotron in an orbit of radius 75 cm at a frequency of 8.0 MHz.What magnetic field magnitude is needed? ,
A) 0.011 T
B) 0.11 T
C) 1.1 T
D) 11 T
E) 110 T

Question

A deuteron has the same charge as a proton but approximately twice the proton mass.Suppose deuterons are being accelerated in a cyclotron in an orbit of radius 75 cm at a frequency of 8.0 MHz.What magnetic field magnitude is needed?  , 
A) 0.011 T 
B) 0.11 T 
C) 1.1 T 
D) 11 T 
E) 110 T

Quizplus · Accepted Answer

The frequency of the deuteron is given as 8.0 MHz. In a cyclotron, the frequency of the magnetic field is given by:
f = qB/(2πm)

where f is the frequency, q is the charge, B is the magnetic field and m is the mass of the particle.

Since the deuteron has the same charge as a proton, q = +1.6 x 10^-19 C.
And since the deuteron has twice the mass of a proton, m = 2 x 1.67 x 10^-27 kg.

Substituting these values into the above equation and solving for B gives:
B = 2πmf/q
B = 2π(2x1.67x10^-27)(8x10^6)/(1.6x10^-19)
B = 1.1 T

Therefore, the magnetic field magnitude needed is 1.1 T, which is choice C.

A Deuteron Has the Same Charge as a Proton but Approximately