# Two particles and magnetic field

1. May 6, 2012

### kimberlyann9

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Bvq=mv^2/r

3. 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?

2. May 6, 2012

### 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?

3. May 6, 2012

### kimberlyann9

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

4. May 6, 2012

### Steely Dan

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

5. May 6, 2012

Thanks!