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Homework Help: Ionization of surrounding air due to metal sphere

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data

    A metal sphere of radius 0.15m carries an initial charge Q1 = +6.4x10-6 Coulombs

    a) show that this amount of charge is insufficient to ionize the surrounding air.

    b) your body, initially neutral, and the soles of your shoes are made of insulating material. You move your finger close to the sphere, without touching the sphere. When your finger gets very close to the sphere (BUT NOT TOUCHING IT) you see a spark in the air between your finger and the sphere. Explain why a spark appears, despite Q1 being insufficient to ionize the air before you brought your finger near.

    c) After seeing the spark, you move your finger away from the sphere. The charge on the sphere is now Q2. Is Q2 less than, equal to, or greater than Q1? Explain briefly.

    d) In terms of the given quantities, what is YOUR net charge now? Explain briefly.

    2. Relevant equations

    E required to ionize air: 3x106 V/m (1 Volt/meter = 1 Newton/Coulomb)

    E of a point charge = (1/4[itex]\pi[/itex]ε0)(Q/r2)

    1/4[itex]\pi[/itex]ε0 = 9x109 Nm2/C2

    3. The attempt at a solution

    a) I was able to answer part A, however, the next 3 parts have me a little confused. For part A, I simply found the Electric Field of the metal sphere which is: (9x109)(6.4x10-6/(0.152)) = 2.56x106 N/C which is the same thing as 2.56x106 V/m...therefore metal sphere's initial charge is not enough (2.56x106 V/m < 3x106 V/m) to ionize the surrounding air.

    b) my attempt for part b is such: despite the fact that your finger is neutral, as you bring it close to the metal sphere which is a conductor, the electrons on the surface of the metal sphere move because they are attracted to the positively charged particles within your finger, however, right before they move, the net electric field due to the metal sphere and your finger exceed the 3x106 V/m required to ionize air therefore the spark occurs....is this in any way close to being correct?

    c) I would assume the charge of the sphere is the same since you did not actually touch the sphere which would have polarized your finger making Q2 less than Q1.

    d) I am assuming for this part your net charge is still 0??

    any help regarding these questions would be greatly appreciated. I have a test on this material in 5 days and this seems to be one of the few concepts that escapes me.
  2. jcsd
  3. Feb 11, 2012 #2


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    Homework Helper

    Welcome to Physics Forums.

    I see a problem, which is that your neutral finger also contains negative particles, which would repel the electrons on the metal sphere.

    For (b), what does your textbook have in the way of discussing insulators, and how charges in insulators might behave when it is near a charged object? A key word to look for is "polarization".

    Well, if the charge is the same, that means Q2=Q1, so you are making a self-contradictory statement here. Did you mean they are the same, or that Q2 less than Q1?

    A question to think about is, what is happening in the spark that was observed?

    And (d) pretty much depends on (c), of course.
    Last edited: Feb 11, 2012
  4. Feb 11, 2012 #3
    b.I think you can also answer this in terms of potential difference(V) between the body and the dome.When the finger is brought nearer to the dome the distance between them(x) decreases and E (E=dV/dx) increases.For a small enough value of x sparking will occur(this can be triggered by the prescence of ionising radiation)
    c.Negative ions produced by the spark will move to the dome to reduce its charge.
    d.Positive ions can move to the body.

    (I think "field emission" can also happen i.e electrons pulled from the finger and to the dome,but I'm guessing this effect will be minimal)
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