Question: Charged droplet in an Electric Field

we encountered a problem where a charged droplet remains stationary above the earth, the electric field of the earth is given and its asks how many excess electrons are in the droplet.

so i assumed that since there is no movement there has to be no net electric field. so i assumed the electric field of the droplet is also 145 n/c just negative. i used the equation kQ/r^2 = electric field. so i multiplied 145 by the square of the radius and i divided it by the constant k to get the total charge of the droplet. then i divided that by 1.602 E-19 to get the number of electrons present, but i still could not get the right answer, what was i doing wrong?

You are right that there has to be zero net something, however, it isn't the Electric field that cancels to suspend the drop, it is the net Force on the droplet that has to be zero to establish static equilibrium. So, let's think about what forces are exerted on the droplet here. Firstly, there is a force of gravity exerted down on the drop since it is suspended above the Earth. Secondly, because the droplet is charged and is in an Electric field, it will feel a force due to this Electric field. We know that this force must point "up" (ie. oppose gravity), so we can determine from this the sign of the charge. Since the Electric field of the Earth points "down" (radially inward, gravity points radially inward), and the direction of the Electric field is defined as the direction of the force on a positive point charge, the charge of the particle will have to be negative. We can now draw a diagram to make this more clear:

The electric force is F_el=qE. We know E (it is given in the problem), and we are looking for q. For the gravitational force we need to do a bit of work if the mass isn't given directly. Since we know the size (radius) of the drop, we can calculate it's mass from the density, ρ, and volume, V=(4/3)πr³: m=ρV. Then we have all the pieces we need.

It should be noted that the equation for the electric field due to a point charge cannot be used in the way you tried to use it. E=kQ/r² is the Electric field due to a point charge with charge, Q, at a distance, r, away.

Hope this is helpful to you, if you have follow-up questions don't hesitate to comment on my answer here. Thank-you for being the first to ask a question!

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A few groundrules...

So, to help keep things on track, I'm going to propose the following groundrules/guidelines:

1. No CAPA questions. Sorry, but the WebTA falls under the same category as the tutorials. I have access to the CAPAs so I will know when you are asking a question from CAPA. Figure out what you don't understand and ask a related question instead.


2. Don't rely only on the webTA. Besides the fact that I likely won't be able to answer all of your questions, I also don't feel that there is any way to implement a web-based help system as effective as talking to a real person. Use this as an additional resource, but take advantage of the tutorials offered and ask a real live TA for help sometimes.


3. No re-posting. Please don't repost the same question over and over, if I didn't answer it, it's because it didn't seem to be a general problem in the class (and you should see a TA), I just simply didn't have the time (and you should see a TA), or I couldn't think of a good way to answer it online (and you should see a real, live, flesh-and-blood TA who can talk and draw and gesture to explain to you).


4. Please no "I have not idea how to do problem # ...". I know that's how it feels, but if you can't do a problem it means you are missing some particular concept. To really help you, I need to know what that concept is. If you just tell me you don't know how to do a problem I can't easily fish out where the real block is, I can just tell you how to do that one particular problem. Ask about the concept in relation to the problem or say what you did and where you got stuck, then I'll be more able to help. :)


5. If you're not in the course, don't pose questions. Sounds harsh, I know... but I only have so much time to work on this. If I find that people from outside the course are drowning out questions from the class I will have to find a way to allow only the members of the class to post, or take down the blog all-together.

I hope we never need any more guidelines than this. I'd rather not have them at all, but I figured it would be better to set some up now than have to keep changing things midstream.

Pre-opening statement

This website is part of an effort to continue, and improve upon last year's webTA project for McGill University's Physics 102 class. Last year, a question and answer section was added part way through the term to augment the examples being posted on my website. The site became so popular by the end of the term we decided to try it again, but with some changes.

I'm hoping that a blog format will help make for a more interactive online environment, in conjunction with the more-or-less static site for examples, explanations etc. We will have to experiment with the best way to work question and answer through the blog, but for now, I plan to essentially "open the floor to questions" on a particular topic. Members of the class can then pose a question regarding the topic by posting a comment on this "floor-opening" post. I will likely not have time to answer all questions (I'm human, and have my own work to do), but when the same questions come up, or a particularly conceptual question is posed, I will try to answer with a new post. From there we can try to have discussions on the topics that people find difficult.

I hope that you will find this new format helpful. I know you can't compare to last year, but your feedback is welcome, and necessary to help the project evolve.