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Homework Help: Squaring units

  1. Feb 8, 2008 #1
    [SOLVED] squaring units

    1. The problem statement, all variables and given/known data
    When you calculate numerically something like q^2/4*Pi*Epsilon_0, do you square the units of q i.e. is it (q 1.602 176 487 × 10-19 C)^2 or q^2 1.602 176 487 × 10-19 C ?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 8, 2008 #2


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    if q = 1.602*10^-19C, then q^2 = {(1.602*10^-19)^2}C^2
  4. Feb 8, 2008 #3


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    A good way to see that you have to square units (or raise them to any power) is to consider the following "paradox".

    Suppose you have $1. One dollar is just 100 cents:

    $1 = ¢100

    If we take the square root of both sides but neglect to take the square root of the units (dollars and cents), we get

    $1 = ¢10!

    So, you have to take the square root of the units too, otherwise all of your dollars are only worth dimes, and all of your dimes are worth a dollar! (As attractive as that might sound, what do you want to bet that the banks would only treat your dollars as being dimes and not vice versa?)
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