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Hello, I have a question regarding the following equation (drift velocity in the electric field). So now I am faced with the next problem, I do not know how I can type in the formula here I just probiers times: m * d ^ 2 x / dt ^ 2 = Q * E - f * v in this formula is the following after changing come out dx / dt = Q * E / (f * 1-e ^ (-f / m * t)) Now, if we multiply by dt, divided toxicity by dx, m divides I still get the following out dx / dt = (Q * E * dt) / (m * dx) - (f * 1) / m but how do I get for now the f under the fraction line from Q * E and then also the Euler number on one side only? I would be much obliged for help. LG =)
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Hello Jacccy welcome here in the forum! Does the differential equation look like this? What is f? One can also write the equation as a differential equation of first order: Please do not send technical questions via PM.
Jacccy wrote: m * d ^ 2 x / dt ^ 2 = Q * E - f * v in this formula is the following after changing to come out dx / dt = Q * E / (f * 1-e ^ (-f / m * t)) You come as close with relocation. Which is a differential equation which has to be integrated once in order to arrive at the speed. I'm assuming that v is supposed to be the speed. With v = dx / dt is then calculated from the second order differential equation, a first order differential equation: dv / dt = Q E / m - v f / m can be solved by means of Vartiation the constants. With the initial condition v (0) = 0 however, I come to v = [1-exp (-f * t / m)] Q e / f looks like a bracket is in your solution set incorrectly.
Yes, that is the coefficient of friction, and dx / dt is really the speed ... but I need NEN moment to understand the XD I'm still not clear with your first step, I can not with d ^ ^ 2 2x/dt deal. So v = dx / dt, that's right now you've written for d ^ ^ 2 2x/dt simply dv / dt, why does it work? And what does it mean when the "^ 2" after the "d" and not after "x" stands for? Does it mean (dx * dx) / dt ^ 2, then when you would v = dx / dt replaced but there are v * dx / dt, or I guess wrong?
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Quote: Does it (dx * dx) / dt ^ 2, then when you would v = dx / dt replaced but there are v * dx / dt, or I guess wrong? Yes, you're thinking wrong It's toxicity like this: The square means that it is the second derivative. Please do not Fachfr