A. Using the information below, calculate the cyclotron period of an electron that is launched into a magnetic field of strength 1 Gauss with a speed 200 m/s. Electron Mass = 9.11 x 10^-31 kg
Proton Mass = 1.67 x 10^-27 kg
Elementary Charge = 1.602 x10^9 Nm/C

b. Using the same information from above, calculate the net work done on the charged particle by the magnetic field as it makes one full rotation.

Explanation:

In cyclotron charged particle moves in a circular path in a magnetic field .

for rotation  

mv² / R = Bqv where m is mass and q be charge of the particle which moves on circular path of radius R with velocity v .

v = BqR / m  

Time period of rotation  

T = 2πR / v  

= 2πR m / BqR

= 2π m / Bq

For electron  

T = 2π x 9.1 x 10⁻³¹ / (1 x 10⁻⁴ x 1.602 x 10⁻¹⁹)

= 35.67 x 10⁻⁸ s  

b )  

work done on the charged particle will be zero because force on charged particle is perpendicular to its movement so work done will be zero