Two particles and magnetic field

[kimberlyann9]

Homework Statement

Two particles, 'A' with charge and mass of q and m and 'B' with charge and mass of -q and 2m, each enter at right angles to a uniform magnetic field with the same velocity. Compare the circular paths that each begin upon entering the magnetic field.

A) A experiences the same force magnitude as that of B and circulates in the same direction as B with A's radius equal to that of B.
B) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius at half that of B.
C) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius equal to that of B.
D) A experiences the same force magnitude as that of B and circulates in the opposite direction as B with A's radius at half that of B.

Homework Equations

Bvq=mv^2/r

The Attempt at a Solution

Since the magnetic field is uniform, B can be disregarded. So can v since it is the same velocity for both particles. So the equation can be reduced to q=m/r, and to rearrange and solve for r, r=m/q. Then I plugged in m and q for both particles and I get A=m/q and B=-2m/q. So B circulates the in opposite direction as A, and A has half the radius as B, so that narrows it down to B and D. I'm a little stuck on the force. Does B experience twice the force magnitude as A because B=2m while A=m?

 

[Steely Dan]

The gyroradius equation comes straight from the Lorentz force law,

$$\vec{F} = q \vec{v}\times\vec{B}.$$

So, what can you conclude about the relative forces?

 

[kimberlyann9]

The gyroradius equation comes straight from the Lorentz force law,

$$\vec{F} = q \vec{v}\times\vec{B}.$$

So, what can you conclude about the relative forces?

They both have the same force magnitude because they both have q for the charge.

 

[Steely Dan]

They both have the same force magnitude because they both have q for the charge.

Exactly. They simply have different motions because they have different masses, and therefore different accelerations when subjected to the same force.

 

[kimberlyann9]

Exactly. They simply have different motions because they have different masses, and therefore different accelerations when subjected to the same force.

Thanks!