- #1

tristanslater

- 14

- 0

## Homework Statement

Ions having equal charges but masses of M and 2M experience a constant electric field while they travel a fixed distance d and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

## Homework Equations

R = mv / qB

## The Attempt at a Solution

The wording of this question is a little ambiguous, but since no values are given for B or E, I figured that the magnetic field was the only one effecting the motion of the particles and that the electric field merely accelerates the particle to the initial velocity.

My thinking was that since the only force is magnetic force causing the circular motion:

F_c = F_B

mv^2 / R = qvB

Solving for R:

R = mv / qB (turns out this is a well established formula)

So, if R = 2Mv / qB (radius of heavy particle), then R / 2 = Mv / qB (radius of light particle in terms of radius of heavy particle.)

My answer: R / 2

However, the correct answer is (unless there is an error) R / sqrt(2).

Can someone explain why?

Thanks.