- #36
frankfjf
- 168
- 0
That's just it though, I'm not sure what to set z to that would make any of the factors zero, due to z being squared on both factors, I can't reliably use negative numbers...
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frankfjf said:Well, I think I can re-arrange the equation if I can't simplify further to be...
(1-3z^2) / (z^2 + R^2)^3/2 in which case z must equal the square root of 1/3?
Factor out (z^2 + R^2)^-5/2 from each term.frankfjf said:Oh, I apologize, that was a typo.
Since we've got f'(x)g(x) + f(x)g'(x), wouldn't that be...
(z^2 + R^2)^-3/2 - 3z^2(z^2 + R^2)^-5/2?
frankfjf said:Regardless, I'll give it a shot. If I factor that out, my guess is I get something like...
(z^2 + R^2)^-5/2[(z^2 + R^2) - 3z^2]
is that correct?
Wait, ah-ha! Now I've got..
(R^2 - 2z^2) / (z^2 + R^2)^-5/2
Set equal to zero, z would have to be R/2^1/2. Since I know R, I can just plug it in now. Rmax = 1.70cm which lines up with the answer given in the book.
Thanks Doc Al and robphy. I apologize for trying your patience and am thankful for your help.
Just for the record, here's how I would finish this starting from the expression in post #29.frankfjf said:So should I abandon the equation I got in post #29?