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I am having a bear of a time getting this equation into Wolfram so I can solve it for E(r) = 1000.

Equation

Equation2

Everything is constant except for little r, which is the cursive r in each term. In case anyone is wondering, this is the expression for the electric field from the center of a hydrogen atom. r is for radius.

Can anyone put this in and link me to the solution? Much appreciated.

user99984
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1 Answers1

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Here is one approach, but you can put in your constants and then play around with defining them using the proper names.

  solve (.2)/(4 pi .5 r^2)(1 - e^(-2 r /.6)(2(r/.6)^2+2(r/.6)+1)) = 1000 for r

See this WA page.

By defining parameters, I mean, something like:

 q = .2, solve (q)/(4 pi .5 r^2)(1 - e^(-2 r /.6)(2(r/.6)^2+2(r/.6)+1)) = 1000 for r

Here you can define your parameters:

q=.2, t = .4, a=.6, solve (q)/(4 pi t r^2)(1 - e^(-2 r /a)(2(r/a)^2+2(r/a)+1)) = 1000

For the parameters you posted, I got two solutions:

  • $\large r = 7.71723 \times 10^{-20}$
  • $\large r = 1.19945 \times 10^{-6}$

Note, there are other options:

  • Get a free CAS like SAGE, Maxima or others. These also have working online copies.
  • Use Mathics.org
Amzoti
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  • Can you solve this for me with q = 1.610^-19, epsilon nought = 8.8510^-12, a = 0.529 * 10^-10. I'm having trouble defining the constants and still getting it to solve. – user99984 Oct 31 '13 at 03:15
  • I got an answer, which was r = 4.76 * 10^-15 m – user99984 Oct 31 '13 at 04:25
  • It is possible I am doing something wrong with the solver, but currently do not see what that is. What did you use? – Amzoti Oct 31 '13 at 04:27
  • My TI 83. I think I can explain what's going wrong with your solver. The function is actually increasing for extremely small values of r, then decreasing for all other ones. Based on some other calculations I did, it should be around the order of 10^-17. – user99984 Oct 31 '13 at 04:59
  • Could you rewrite for me your equation in ASCII form ? I am almost blind and I cannot read the front term. – Claude Leibovici Oct 31 '13 at 05:12
  • I am not sure what you mean by ASCII – Amzoti Oct 31 '13 at 05:13
  • In words, I have $q$ divided by the product $4 \times \pi \times t \times r^2$. Is that the term you were speaking of? – Amzoti Oct 31 '13 at 05:15
  • At the front end of the equation, I defined each parameter and its value (I used small values and it works. When I change to the value you wanted, it goes south on me and I am trying to figure out why. – Amzoti Oct 31 '13 at 05:21
  • @ClaudeLeibovici: Okay, got my solver working. For the parameters you provided, it found two solutions. $r = 7.7172310^{-20}$ or $r = 1.1994510^{-6}$ Still not sure how to get Wolfram Alpha to do it. Regards – Amzoti Oct 31 '13 at 05:46
  • @user99984: I added the results for the values you asked. – Amzoti Oct 31 '13 at 06:04
  • Excellent, the first value is close to what I would expect. How did you get these? – user99984 Oct 31 '13 at 08:44
  • Ooh! sliders too! +1 – amWhy Oct 31 '13 at 12:08
  • I see you're up at 5:00 am to catch you morning fix! ;-) – amWhy Nov 01 '13 at 12:01
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    Yes, yesterday was fun - seeing all the little "goblins", and a few not so little goblins! – amWhy Nov 01 '13 at 12:06