Circular Motion in a Simple Mass Spectrometer

[Oribe Yasuna]

Homework Statement

In the simple mass spectrometer shown in the figure below, positive ions are generated in the ion source. They are released, traveling at very low speed, into the region between two accelerating plates between which there is a potential difference ΔV. In the shaded region there is a uniform magnetic field B

; outside this region there is negligible magnetic field. The semicircle traces the path of one singly charged positive ion of mass M, which travels through the accelerating plates into the magnetic field region, and hits the ion detector as shown.

Determine the appropriate magnitude and direction of the magnetic field B

, in terms of the known quantities shown in the figure below (in addition to M and q, where q is the charge on an ion).

Magnitude B = ?
direction = ?

Homework Equations

F_mag = dp/dt_mag = qvB
dp/dt_mag = p(v/R) = p(omega), p = ymv
omega = q_mag * b / (ym)

The Attempt at a Solution

deltaV (I don't know what to do with electrical potential)
M (mass)
q (charge)
d/2 = R (radius)
v << c, y = 1, p = mv (approximation)

F_mag = dp/dt_mag
qvB = p(v/R)
qvB = p(v/(d/2))
qB = p/(d/2))
B = p/(d/2))/q
B = 2p/dq, p = mv (approx.)
B = 2Mv/dq

This is wrong, probably because I'm not given velocity. However, I don't know how to get magnetic field without velocity? I think the problem is I don't know what to do with electric potential.

 

[gneill]

Your ion with charge q is accelerating through the ΔV between the plates. Look for an equation relating the energy acquired by an electric charge accelerating through a potential difference.

 

[Oribe Yasuna]

1/2 mv^2 = q deltaV

This kinetic energy equation?

mv^2 = 2q deltaV
v^2 = 2q deltaV / m
v = sqr rt (2q delta V / m)

 

[Oribe Yasuna]

deltaV = Ed

But I'm missing both E and d? d is the separation between the plates but the variable d in the image seems to be a length.

 

[gneill]

deltaV = Ed

But I'm missing both E and d? d is the separation between the plates but the variable d in the image seems to be a length.

There's another equation that involves the charge.