- #1
Samkiwi
- 16
- 1
- Homework Statement
- I'm having trouble finding the proof of the relativistic acceleration formula starting from the velocity formula, I've been working on it for a long time but I can't solve this question. :)
- Relevant Equations
- electromagnetism and relativity
It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other.
Here's the questionA possible expression of speed as a function of time is the following:
$$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A =\frac{qE}{m}$$
Taking into account that [2] can be written in the equivalent form.
$$\frac{dv}{dt}=\frac{qE}{m}(1-\frac{v^{2}}{c^{2}})^{-\frac{3}{2}}[3]$$
verify by deriving and substituting that the function v (t) defined by [2] satisfies [3]
Here's the questionA possible expression of speed as a function of time is the following:
$$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A =\frac{qE}{m}$$
Taking into account that [2] can be written in the equivalent form.
$$\frac{dv}{dt}=\frac{qE}{m}(1-\frac{v^{2}}{c^{2}})^{-\frac{3}{2}}[3]$$
verify by deriving and substituting that the function v (t) defined by [2] satisfies [3]
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