Homework Help: Motion of a hydrogens ions

1. Dec 16, 2008

eoghan

1. The problem statement, all variables and given/known data
Some hydrogens and deuterium ions are accelerated by a potential difference V. These ions entered then in a region with a magnetic field B orthogonal to their velocity. In the position H and K (along the axis parallel to the velocity) there are two sensors and the distance between them is d. Find the the V you need to make the hydrogen ions go towards H and deuterium towards K

2. Relevant data
d=0.8cm
B=0.4T
q(e)=1.6*10(-19)
m(H)=1.67*10^-27
m(D)=3.34*10^-21Kg

3. The attempt at a solution
Velocity of the ions after the acceleration by a potential difference V:
qV(1)=1/2mv^2+qV(2) ==> v=sqrt[(2qV)/(m)] where m is m(D) or m(H)

motion of the ions in the magnetic field: circular motion with radius:
r(D)=v(D)m(D)/qB
r(H)=v(H)m(H)/qB

The distance between the two sensors is d, so r(D)-r(H)=d ==> 4qV=dqB ==> V=0,00008V

Is this right?

2. Dec 16, 2008

Redbelly98

Staff Emeritus
Without seeing a figure of the magnetic field region, we can't say.

By any chance are the ion trajectories 90 degrees, or 1/4, of a full circle?

3. Dec 16, 2008

eoghan

It's 1/2 circle

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4. Dec 16, 2008

Redbelly98

Staff Emeritus
Okay, that makes more sense now.

The distance between H and K is not the difference in radii of the two circles. Can you look at the figure again and see how that distance does relate to the circles?

5. Dec 16, 2008

eoghan

Is it the difference between the diameters?

6. Dec 16, 2008

Redbelly98

Staff Emeritus
Yes.

7. Dec 18, 2008

eoghan

Now it works... thanks!