Particle 1, with mass 5.0 u and charge +2 e , and particle 2, with mass 3.0 u an
ID: 2259640 • Letter: P
Question
Particle 1, with mass 5.0 u and charge +2e, and particle 2, with mass 3.0 u and charge +3e, have the same kinetic energy and enter a region of uniform magnetic field B, moving perpendicular to B. What is the ratio of the radius r1 of the particle 1 path to the radius r2 of the particle 2 path?
Explanation / Answer
magnetic force = centripetal force
Bq v = m v^2 /r
r = m v / q B ; same field ( B)
r = m v / q
Now, same K.E. = 1/2 * m * v^2 for both particles
which implies, 1/2 m1 v1^2 = 1/2 m2 v2^2
5 * v1^2 = 3 * v2^2
v1/v2 = sqrt ( 3/5)
m1/m2 = 5 /3
q1/q2 = 2/3
plug into above equation,
r1/r2 = m1/m2 * v1/v2 * q2/q2
= 5/3 * sqrt(3/5) * 3/2 = 1.93