Charged particle movement close to single charged plate

[pchama1]

Hi everybody.
I am a mechanical engineer trying to do an electrical experiment.
I wonder if anybody can help me with an advice.

Here is my experiment. I have a single rectangular metal plate to which I apply a known high negative voltage DC. Not sure yet what that voltage is going to be. Let's say 10kV. Next, I bombard the plate with negatively charged water droplets flying into the plate at 200 miles per hour. Here is my question. Will electrostatic force between the plate and the droplets be high enough to deflect the droplets away from the plate ? The droplet diameter is let's say 20 microns. I do not know yet its charge but I am pretty sure I will be able to vary it.

Is there any way to calculate the electrostatic force applied to the droplet as it approaches the plate ?

Thank you

 

[GRDixon]

Hi everybody.
I have a single rectangular metal plate to which I apply a known high negative voltage DC. Not sure yet what that voltage is going to be. Let's say 10kV. Next, I bombard the plate with negatively charged water droplets flying into the plate at 200 miles per hour. Here is my question. Will electrostatic force between the plate and the droplets be high enough to deflect the droplets away from the plate ? The droplet diameter is let's say 20 microns. I do not know yet its charge but I am pretty sure I will be able to vary it.

Is there any way to calculate the electrostatic force applied to the droplet as it approaches the plate ?

Thank you

The electric force experienced by a droplet will just be the droplet's excess charge multiplied by the plate's electric field. The plate's electric field can be calculated from its voltage, provided your drop is coming into the middle of the plate's surface and you're not too far away from the plate. For the other information, such as your droplet's diameter, etc., and how they factor into the experiment, I suggest you Google (or read about) Millikan's oil drop experiment. You'll find useful formulas relating droplet diameter and drag, etc., there.

 

[pchama1]

The electric force experienced by a droplet will just be the droplet's excess charge multiplied by the plate's electric field. The plate's electric field can be calculated from its voltage, provided your drop is coming into the middle of the plate's surface and you're not too far away from the plate. For the other information, such as your droplet's diameter, etc., and how they factor into the experiment, I suggest you Google (or read about) Millikan's oil drop experiment. You'll find useful formulas relating droplet diameter and drag, etc., there.

Thank you GRDixon. In Millikan's experiment he used two plates parallel to each other. It is easy to calculate the electric field for two plates. But how to obtain an electric field for a single blade given the know voltage applied?

 

[GRDixon]

Thank you GRDixon. In Millikan's experiment he used two plates parallel to each other. It is easy to calculate the electric field for two plates. But how to obtain an electric field for a single blade given the know voltage applied?

What if a parallel plate capacitor were charged up using a battery, and the plates were then isolated from the battery terminals. As you state, you know how to calculate the electric field between the plates. Now remove one of the plates a large distance away. Would the electric field from the remaining plate be half of what it is with both plates in place? I'm not sure. In any case, in my first answer I assumed that the test charge was relatively insignificant, and wouldn't result in a buildup of opposite-sign charge on the single plate. If this assumption isn't good, you'd have to use the method of images to calculate the E field between the test charge and the plate. Sorry I can't be of more help. I did a cursory walkthrough of a couple of texts, and didn't find any discussion of the E field of a single plate, raised to a potential V.