Two charged particles are accelerated through a uniform electric field and zero magnetic field, then enter a region with zero electric field and a uniform magnetic field. The particles start at rest from the same position (but at different times; they do not interact with each other). They have identical charges, but different masses. Particle 2 has a cyclotron radius 1.5 times as large as that of particle 1. Find ratio m2/m1

In magnetic field, charged particle will have circular path. Let the radius of their circular path be r₁ and r₂. Let their velocity at the time of entering magnetic field be v₁ and v₂.

The velocity with which they will come out of electric field can be measured from following equation

Eq = 1/2 m v², E is electric field, q is charge on the particle, m is mass and v is velocity.

v² = 2Eq / m

radius of circular path can be measured by the following expression

m v² / r = Bqv

2Eq / r = Bqv

r = 2Eq / Bqv

= 2E / Bv

r² = 4E² / B²v²

= 4E²m / B²x 2Eq

since E, B and q are constant

r² = K. m

r₂² / r₁² = m₂ / m₁

1.5²

m₂ / m₁ = 1.5²

= 2.25