Four particles enter a region of uniform magnetic field with velocities perpendicular to magnetic field lines. The particles have the following masses and charges: 1 : charge q; velocity v and mass m
2: charge 29 velocity 2v and mass 2m
3: charge q: velocity 3v, mass m/2
4: charge 2q: velocity 30, mass 2m
Rank the radii of theirs paths for these particles, largest to smallest

r4 > r2 > r3 > r1

Explanation:

correction of the statement:

The particles have the following masses and charges:

1 : charge q; velocity v and mass m

2: charge 2q velocity 2v and mass 2m

3: charge q: velocity 3v, mass m/2

4: charge 2q: velocity 3v, mass 2m

In order to calculate the radius of the trajectories of the four particles, you use the following formula for the radius of the trajectory of a particle in a perpendicular and constant magnetic field:

                (1)

m: mass of the particle

v: speed of the particle

q: charge

B: magnitude of the magnetic field

Then, in comparison with the equation (1), you obtain for each case:

1 : charge q; velocity v and mass m

= r

2: charge 2q velocity 2v and mass 2m

3: charge q: velocity 3v, mass m/2

4: charge 2q: velocity 3v, mass 2m

By the previous results you can conclude:

r4 > r2 > r3 > r1