Moving Charges and Magnetism Problem

[anraphy]

Homework Statement

Two particles A and B having equal charges +6C, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular path of radii 2 and 3cm repectively. The ratio of mass of A and B is ______

Homework Equations

Force on the particle in a magnetic field = Bqv

In a circular path, mv^2/r = Bqv
→r = mv/Bq

The Attempt at a Solution

I don't know if I should consider their velocities to be equal.
If the velocities are equal, the r(A)/r(B) = 2/3 which is incorrect.

 

[TSny]

Hello, anraphy. Welcome to PF!

Do you know how to relate the final speed of a particle to the potential difference through which it is accelerated?

 

[anraphy]

Potential Difference and Velocity

Hello, anraphy. Welcome to PF!

Do you know how to relate the final speed of a particle to the potential difference through which it is accelerated?

E = Vq
→0.5mv^2=Vq
→v = √(2Vq/m)
OR
→V=0.5mv^2/q

where
V-potential difference
m-mass of the particle
v-velocity of the particle
E-energy of the particle
q-charge on the particle

 

[TSny]

OK. Good. Can you see how to use that?

 

[Nero26]

Hello, anraphy
The particles have different masses but have equal charge.So when it's accelerated through same potential difference, they will gain equal electric energy=Vq=kinetic energy
Vq=.5m₁v₁²=.5m₂v₂²
∴m₁/m₂=(v₂/v₁)²
Similarly when entering in Magnetic field due to different velocities they will follow different circular path of radii r_a,r_b respectively.
m₁v₁/r_a=m₂v₂/r_b=qB

 

[anraphy]

I think I got it. Thank You :)

 

[TSny]

View attachment 72219

I think I got it. Thank You :)

Looks right. Nice work.