Question

The first practical cyclotron developed by Lawrence and Livingston in 1932 had dees of radius 12 cm and produced protons of about 1 MeV energy. 

Calculate :

(i) the applied magnetic induction 

(ii) the frequency of the accelerating electric field.

[m^p = 1.67 × 10^-27 kg, q = 1.6 × 10^-19 C]

Answer 1

Data: R = 0.12 m, 

m^p = 1.67 × 10^-27 kg, 

q = 1.6 × 10^-19 C,

KE_max = 1 MeV =(1 × 10⁶)(1.6 × 10^-19) 

= 1.6 × 10^-13 J

(i) KE_max = \(\cfrac{q^2(BR)^2}{2m}\)

\(\therefore\) The applied magnetic induction,

(ii) The frequency of the applied electric field (cyclotron frequency),