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Q. Two identical charged particle A and B initially at rest are accelerated by a common potential difference V. They enter into a transverse magnetic field B and describes a circular path of radii r1 and r2 respectively then what is their Mass ratio?

Q. Two identical charged particle A and B initially at rest are accelerated by a common potential difference V. They enter into a transverse magnetic field B and describes a circular path of radii r1 and r2 respectively then what is their Mass ratio?

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
As the particles start from rest, kinetic energy would be the work done on the particle by V, lets assume the charge on the particle is q, then
(1/2)m1v12 = qV  and
(1/2)m2v22 = qV
 
  • m1v12 = m2v22   ----- (1)
 
Magnetic force on each particle = Centripetal force on the particle
  •  m1v12 /R1 = qBv1  
  • v1 = qBR1/m1
Similarly,
  •   v2 = qBR2/m2
  • When we put the value in equ 1 we get,
  • m1 (qBR1/m1)2 = m2 (qBR2/m2)2
  • R12/m1 =  R22/m2
  • m1/m2 =  R12/R22

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