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Electrostatics: Creating Charged Objects

  1. Feb 20, 2012 #1
    An iron arrowhead has an initial charge of 2.100e-6 C. How many electrons are required to give it a charge of −2.82 μC?

    I know that e (the elementary charge) = +/- 1.602E-19 C
    And N is the number (or excess charge)

    I tried solving this problem 2 ways. The first way:

    (2.100E-6 - 2.82E-6)/1.602E-19
    I got 4.45E12 electrons

    The second way I did:
    2.100E-6-1.602E-19 * N = -2.82E-6
    -1.602E-19 * N = -2.82E-6 - 2.100E-6
    N =-4.92E6/-1.602E19
    N= 3.05E25 electrons

    However, my homework says it's wrong I tried typing them in with a negative sign, it's wrong. I tried rounding to the nearest electrons, still wrong.
    What am I doing wrong? I really have no idea!
     
  2. jcsd
  3. Feb 20, 2012 #2

    SammyS

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    The arrowhead initially has a positive charge. The first 2.100×10-6 C worth of electrons are needed to neutralize the initial positive charge.
     
  4. Feb 20, 2012 #3
    You begin with a charge of 2.1e(-6) C. You need to add electrons until you have a charge of -2.82e(-6) C. This means you need to add enough electrons such that the total charge of all the electrons added is equal to the difference in these charges; that is, the total charge of all the eletrons you add must be [2.1e(-6) - (-2.82e(-6)] C.
     
  5. Feb 21, 2012 #4
    So would I divide 2.100E-6 by -1.602E-19?
     
  6. Feb 21, 2012 #5
    So 7.27E-7. What do I do from there?

    I only have a couple tries left on my homework and I want to get it right.
     
  7. Feb 21, 2012 #6
    I believe you have found the difference in charge incorrectly; you did 2.1e(-6) - 2.82e(-6) but you need to make it 2.1e(-6) - (-2.82e(-6)) so that it becomes addition and you get:

    2.1e(-6) + 2.82e(-6) = 4.92e(-6) C

    So the total number of electrons required woul have charge equal to 4.92e(-6). So what would you do next?




    [Another way to think about it is that you need x electrons to reduce the charge from 2.1e(-6) to 0 and then another y electrons to reduce the charge from 0 to -2.82e(-6). If you sum x and y together you should find the same number as you will from the method I explained above.]
     
  8. Feb 21, 2012 #7
    Wouldn't I divide that number by e? Then I get 3.07E13 electrons.
     
  9. Feb 21, 2012 #8
    Yes, that is correct. You can try it the second way I mentioned to convince yourself that they are equivalent.
     
  10. Feb 21, 2012 #9
    I was holding my breath as I typed it into my answer key, waiting for the check! Thanks so much! I really appreciate it!
     
  11. Feb 21, 2012 #10
    I'm glad to have been of assistance. Hopefully you've learned something from this. :)
     
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