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~christina~

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**[SOLVED] Electric field and particles**

## Homework Statement

It is useful to separate fast-moving ions from slow-moving ones. To accomplish this, the ions enter a component of a device (modeled somewhat like a velocity selector) as a narrow horizontal beam that passes between two parallel plates that are

**5.0 cm**long and

**4.0 cm wide**. The separation between the plates is

**3.0 cm**. A high voltage applied to the plates accelerates the ions toward one of the plates and away from the other plate. This ion beam consists of a mixture of [tex]SO_2^{4+}[/tex] particles. These particles enter the space between the plates having initial velocities

**5.60 × 04 m / s**and

**5.60 × 105 m / s**in the positive x-direction. The mass of each ion is

**1.06 x 10-25 kg**and the applied potential is

**150 V**. The ions enter the space between the plates at its center. After leaving this space, the ions travel an additional 50 cm to the detector

(a) Give a brief description of the electric field between the plates if the ions' motion is in the positive xy-plane after leaving the gap.

(b) Calculate the magnitude of the acceleration that the particles have when they are between the plates.

(c) Find the angle(s) of the particles, relative to their initial motion, when they emerge from the plates.

(d) Will these ions strike the detector at the same spot? If yes, what is the y-coordinate of the ions; if no, what is the separation between the ions when they strike the detector? Ignore the gravitational force.

http://img231.imageshack.us/img231/5209/picture2bm2.th.png [Broken]

## Homework Equations

[tex]F= qE[/tex]

[tex]\Delta V= -Ed[/tex]

[tex]a= \frac{qE} {m}[/tex]

## The Attempt at a Solution

I'm not sure what they mean by mix of particles of [tex]SO_2^{4+}[/tex] with different velocities since I thought that would be one molecule but I think that they mean that it is different charges thus different velocities so I would calculate them seperately.

[tex]m_{1&2}= 1.06 x 10-25 kg [/tex]

[tex]v_1= 5.60 × 04 m/s [/tex]

[tex]v_2= 5.60 × 105 m/s[/tex]

[tex]\Delta V= 150V [/tex]

**a) Give a brief description of the electric field between the plates if the ions' motion is in the positive xy-plane after leaving the gap.**

Not sure but would it be a good description if I said that the electric field goes from + to - and if the ion's molecules are going in the possitive xy direction, then the possitive plate must be on the bottom and the negative plate on the top.

**(b) Calculate the magnitude of the acceleration that the particles have when they are between the plates.**

[tex]\Delta V= -Ed [/tex]

[tex]150V=E(0.03m) [/tex]

[tex]E= 5e3 [/tex]V/m

[tex]a= \frac{qE} {m}[/tex]

__I have E but don't have q and I'm not sure how to find it either for both the particles (not sure if one is + and other - [very confusing]). (I don't think it would be the same as a electron)__

**(c) Find the angle(s) of the particles, relative to their initial motion, when they emerge from the plates.**

not sure how to find this...

do I use the UAM equations after I find the accelerations? (not sure how to relate that to when they exit)

**(d) Will these ions strike the detector at the same spot? If yes, what is the y-coordinate of the ions; if no, what is the separation between the ions when they strike the detector? Ignore the gravitational force.**

not sure how to find this either.

Help please

Thanks

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