Solve failing and not clear why

Question

I define the function:

 w[q_, n_, a_] := q/(4 Pi n r^2) (1 - Exp[-2 r/a] (2 (r/a)^2 + 2 (r/a) + 1))

I then want to solve:

 q = 1.6*10^(-19);
 n = 8.85*10^(-12);
 a = 0.529*10^(-10);
 Solve[w[q, n, a] == 1000, r]

This does not work and I do not understand why. I think there is a solution. Any ideas?

Nasser · Accepted Answer · 2013-10-31 05:59:54Z

3

Use Reals option with Solve since you did not use exact numbers. You'll get an answer (also with Solve::ratnz) along with it

Solve[w[q, n, a] == 1000, r, Reals]

Mathematica graphics

answered Oct 31 '13 at 5:40

Nasser

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$\begingroup$ Thank you. You show NSolve, but Solve works. Why does your display show the result in that long form as opposed to mine showing it in scientific notation? $\endgroup$ – Amzoti Oct 31 '13 at 5:50
$\begingroup$ @Amzoti sorry, copied the wrong command. It is Solve, not NSolve. I tried NSolve earlier also to see what it does. But ended up using Solve with Reals. $\endgroup$ – Nasser Oct 31 '13 at 5:59

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