Uniform Magnetic Field question

[Garmeth]

Homework Statement

I have a physics final coming up and instead of problems, the final will cover multiple choice conceptual questions.

"Several identical charged particles, each with charge Q and mass M, move in a region of uniform magnetic field B. The only force any of the particles experience is the magnetic force due to this field; consequently they are all traveling on circular paths of different radii and different speeds.

Question : The periods- the times the particles take to complete circles- are

A) greater for the particles moving on larger circles;

B) smaller for the particles moving on larger circles;

C) Smaller for the particles moving at higher speeds;

D) Greater for the particles moving at higher speeds;

E) The same for all particles.

The answer is apparently E but I put A.

Homework Equations

Force on a point charge due to a magnetic field

F=qvbSin(theta)

Magnetic force = Centripetal Force

qvbSin(theta) = Mv(squared)/r

The Attempt at a Solution

I'm having huge troubles understanding this problem and the significance of the different radiis and velocities. If magnetic force = Centripetal force, which it does because the only force causing these charges to move in a circle is the magnetic field, then the bigger R gets the weaker the field becomes, which makes sense. The weaker the field the slower the charge should be going, which also makes sense. So the further away the charge gets from the field, the weaker the force, the slower the speed, the more distance to travel, so period or the time the particle takes to complete its circle should be greater. However, the answer is E?

-Thanks in advance.

 

[xlava]

qvB = mv^2/r
qB = mv/r

r = mv/qB

period = 2pir/v

period = 2Pm/qB

so, as mass increases, period increases, as charge increases period decreases.

each have the same mass and charge, so each have the same period in the same field. Period is independent of radii.