Question

A positive tau (τ⁺, rest energy = 1777 MeV) is moving with 2025 MeV of kinetic energy in a circular path perpendicular to a uniform 1.15 T magnetic field.

(a) Calculate the momentum of the tau in kilogram-meters per second. Relativistic effects must be considered.

kg · m/s

(b) Find the radius of the circular path.

m

Answer 1

Given

   rest energy E _o= 1777 MeV =1777*( 1.6*10^-13 ) J

   kinetic energy E = 2025 MeV = 2025 *(1.6*10^-13 ) J

   magnetidc field B = 1.15 T

   velocity of light c = 3*10⁸ m/s

   charge of the particle q =1.6*10^-19 C

      

mass of the praticle m_o = E_o / c²

a)   

the momentum of the tau is given by

p = √ ( 2m_oE)

p = √(2*E_o*E/c²)

P = √ (2*2025 *1.6*10^-13 *1777 *1.6*10^-13 )/(3*10^8)

P = 1.430*10^-18 kg.m/s

b)    

the radius of the circular path is given by

r = p / ( qB)

r = 1.430*10^-18/(1.6*10^-19*1.15)

r = 7.77 m