Recent content by Radek Vavra

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    An Integral With A Square Root In The Denominator

    How would you integrate it? \int \frac{d \varphi}{\sqrt{1 + \frac{a^2 b^2 \sin^2 \alpha}{(a \sin \varphi + b \sin (\alpha - \varphi))^2}}} I know that solving it numerically would probably be easier, but I would prefer a closed form solution in this case.
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    A Difficult Differential Equation

    I've noticed :) I'm currently trying to integrate the changed equation.
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    A Difficult Differential Equation

    So, as a result of a thought experiment, I've got a differential equation, which I can't solve: R r'' \sin \frac{r}{R} - 2 (r')^2 \cos \frac{r}{R} - R^2 \cos \frac{r}{R} \sin^2 \frac{r}{R} = 0 , R > 0 To make the matters worse, the function r(\varphi) will probably depend on multiple...
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    A Problem with Two Current-Carrying Wires

    We all know that there is a force between them. But I wonder... if electrons in both wires are moving with the same speed the relative velocity between the electrons in wire A and B equals zero - but then there would be no magnetic field and no force. Could you help me with this?
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