How to Calculate Voltage for Hydrogen and Deuterium Ions in a Magnetic Field?

[eoghan]

Homework Statement

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

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?

 

[Redbelly98]

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?

 

[eoghan]

It's 1/2 circle

 

[Redbelly98]

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?

 

[eoghan]

Is it the difference between the diameters?

 

[Redbelly98]

Yes.

 

[eoghan]

Now it works... thanks!