Determining asymptotic approach

  • Thread starter mmwave
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I need to "determine the asymptotic approach of v to c, correct to powers of 1/t^2" in the equation below.

[tex]v = \frac{eEt/m_o}{\sqrt{1 + (eEt)^2/(m_oc)^2}}[/tex]

Clearly the asymptote is c (speed of light) and I think I'm being asked to find an expression like constant * (1 + a1 / t + a2 / t^2 + ...) but I have not been able to do so. Power series don't work and binomial thm doesn't apply. Please help.
 

arildno

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1. Rewrite your expression as:
[tex]v=\frac{c}{\sqrt{1+\epsilon}},\epsilon=\frac{(m_{0}c)^{2}}{(eEt)^{2}}[/tex]
2. Make a power series expansion in [tex]\epsilon[/tex]
 
211
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Thanks Arildno. I guess I should have studied calculus in Norway.

Once I followed your advice I could also see that for any particle capable of reaching v approx. equal to c, I can use the binomial theorem.
 

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