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[quote="Ricky"]naja ich weiss, dass die divergenz eines vektorfeldes folgendermaßen definiert ist. Aber ich weiss nicht wirklich, wie ich nun damit die divergenz zu meinem vektorfeld berechnen soll... :help:[/quote]
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<table border="0" cellpadding="3" cellspacing="1" width="100%" class="forumline"> <tr> <th class="thCornerL" width="22%" height="26">Autor</th> <th class="thCornerR">Nachricht</th> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 17:27<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">ok vielen lieben dank. <img src="images/smiles/up.gif" alt="Thumbs up!" border="0" /> <img src="images/smiles/prost.gif" alt="Prost" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 16:35<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ja, aber <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\epsilon_0"> lässt du lieber als Konstante stehen oder du schreibst <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\approx "> und fügst bei dem Zahlenwert Einheiten hinzu.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 16:26<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">also wäre das dann doch : <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\operatorname{div} \vec E = \frac{\rho(r)}{\epsilon_0}"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\rho(r)=\operatorname{div} \vec E \cdot {\epsilon_0}"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\rho(r)= \left(E_0 \cdot \frac{2}{r}\right) \cdot \epsilon_0"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\rho(r)= \left(E_0 \cdot \frac{2}{r}\right) \cdot 8,85 \cdot 10^{-12}"> <br /> <br />wäre das dann so richtig...?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 11:07<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Genau: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\operatorname{div} \vec E = \nabla \cdot \vec E(r) = \frac{\rho(r)}{\epsilon_0}"> <br /> <br />Da du die Divergenz schon berechnet hast, kannst du das doch in diese Gleichung einsetzten und einfach nach <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\rho(r)"> auflösen.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 10:59<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ich weiss nicht, ob mir das weiterhilft, aber ich habe herausgefunden, dass <br /> <br />folgender Zusammenhang gelten soll... <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?div E(r)=\frac{1}{\epsilon_o}\cdot \rho(r)"> <br /> <br />bzw: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\rho (r) = div E(r) \cdot \epsilon_0"> <br /> <br />stimmt das... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /> <br /> <br />falls ja, wie bringt mich das nun weiter...denn <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\epsilon_0"> <br /> <br />ist doch einfach nur eine Konstante mit dem Wert <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?8,85\cdot 10^-{12} \frac{As}{Vm}"> <br /> <br /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /> <img src="images/smiles/help.gif" alt="Hilfe" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 10:33<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>pressure hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">Und für die Aufgabe b) musst du dir nur mal die Maxwell-Gleichungen anschauen, insbesondere wie die Divergenz vom elektrischen Feld mit der Ladungsverteilung zusammenhängt.</td> </tr></table><span class="postbody"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 10:31<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ja, klar der Vorfaktor gehört noch dazu. <img src="images/smiles/up.gif" alt="Thumbs up!" border="0" /> <img src="images/smiles/prost.gif" alt="Prost" border="0" /> <br /> <br />Vielen lieben Dank! <img src="images/smiles/up.gif" alt="Thumbs up!" border="0" /> <br /> <br />Wäre es dann vielleicht möglich, dass wir aufgabenteil b) auch noch <br /> <br />zusammen machen...denn da weiss ich noch nicht einmal einen Ansatz... <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /> <img src="images/smiles/help.gif" alt="Hilfe" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 09:42<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img src="images/smiles/up.gif" alt="Thumbs up!" border="0" /> - Allerdings fehlt natürlich noch der Vorfaktor <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?E_0"> !</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 09:42<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">ach ja, dann wäre das : <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\nabla \cdot \vec E = \frac{1}{r} - \frac{x^2}{r^3} + \frac{1}{r} - \frac{y^2}{r^3} + \frac{1}{r} - \frac{z^2}{r^3} = \frac{3}{r} - \frac{x²}{r^3}-\frac{y²}{r^3}-\frac{z²}{r^3} = \frac{3}{r}-\frac{x²+y²+z²}{r^3}= \frac{3}{r}-\frac{r²}{r^3}=\frac{3}{r}-\frac{1}{r} = \frac{2}{r} "> <br /> <br />ok... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 09:34<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Noch nicht ganz: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{r}+\frac{1}{r}+\frac{1}{r} \neq \frac{3}{3r} = \frac{1}{r}"> <br /> <br />Und für die Aufgabe b) musst du dir nur mal die Maxwell-Gleichungen anschauen, insbesondere wie die Divergenz vom elektrischen Feld mit der Ladungsverteilung zusammenhängt.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 23. Apr 2011 08:55<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">ok, dann wäre das also <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\nabla \cdot \vec E = \frac{1}{r} - \frac{x^2}{r^3} + \frac{1}{r} - \frac{y^2}{r^3} + \frac{1}{r} - \frac{z^2}{r^3} = \frac{3}{3r} - \frac{x²}{r^3}-\frac{y²}{r^3}-\frac{z²}{r^3} = \frac{3}{3r}-\frac{x²+y²+z²}{r^3}= \frac{1}{r}-\frac{r²}{r^3}=\frac{1}{r}-\frac{1}{r} = 0 "> <br /> <br />ist das nun so richtig...? <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Namenloser</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 21:04<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">sieht richtig aus, aber ist noch nicht ganz "fertig" du kannst das noch weiter zusammenfassen. <br /> <br />lass die klammern weg und überleg dir was x²+y²+z² ist, bzw welches andere zeichen du dafür kennst(tipp: fängt mit r an)</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 19:58<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Achso ok. <img src="images/smiles/up.gif" alt="Thumbs up!" border="0" /> <br /> <br />Also wäre das dann für die anderen beiden komponenten analog : <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{\dd}{\dd x} \left(\frac{x}{\sqrt{x^2+y^2+z^2}} \right) =\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{x^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3} "> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{\dd}{\dd y} \left(\frac{y}{\sqrt{x^2+y^2+z^2}} \right) =\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{y^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3} "> <br /> <br />und <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{\dd}{\dd z} \left(\frac{z}{\sqrt{x^2+y^2+z^2}} \right) =\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{z^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3} "> <br /> <br />sodass insgesamt folgt : <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\nabla \cdot \vec E = \partial_x E_x + \partial_y E_y + \partial_z E_z=\left(\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{x^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3}\right) + \left(\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{y^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3}\right) + \left(\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{z^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3}\right)"> <br /> <br />und nun das ganze wieder mit r : <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\nabla \cdot \vec E = \left(\frac{1}{r} - \frac{x^2}{r^3}\right) + \left(\frac{1}{r} - \frac{y^2}{r^3}\right) + \left(\frac{1}{r} - \frac{z^2}{r^3}\right) "> <br /> <br />richtig nun... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <br /> <br />und falls das nun so richtig ist, würdest du mir dann auch noch bei <br /> <br />aufgabenteil b) helfen... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/prost.gif" alt="Prost" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 19:44<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Nein, das hoch 1/2 steckt ja schon in der Wurzel.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 19:11<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">wow super vielen lieben dank. Das ist wirklich toll, dass du mir so hilfst und das alles so ausführlich aufgeschrieben hast. Aber ich habe mal eine frage und zwar müsste das ergebnis nicht <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{x^2}{\left(\sqrt{x^2+y^2+z^2}\right)^{\frac{3}{2}}} "> <br /> <br />lauten... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 17:51<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ich lass mal alles unnötige weg: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\frac{\dd}{\dd x} \left(\frac{x}{\sqrt{x^2+y^2+z^2}} \right) \underbrace{=}_{Produktregel} \left(\frac{\dd}{\dd x} x\right)\frac{1}{\sqrt{x^2+y^2+z^2}} +x \cdot \left(\frac{\dd}{\dd x}\frac{1}{\sqrt{x^2+y^2+z^2}}\right) \\ \underbrace{=}_{Kettenregel} \frac{1}{\sqrt{x^2+y^2+z^2}} - x \cdot \frac{1}{\left(\sqrt{x^2+y^2+z^2}\right)^2} \cdot \left(\frac{\dd}{\dd x} \sqrt{x^2+y^2+z^2}\right) \\ \underbrace{=}_{Kettenregel} \frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{x}{\left(\sqrt{x^2+y^2+z^2}\right)^2} \cdot \left(\frac{2x}{2 \cdot \sqrt{x^2+y^2+z^2}}\right) \\ =\frac{1}{\sqrt{x^2+y^2+z^2}} - \frac{x^2}{\left(\sqrt{x^2+y^2+z^2}\right)^3} "></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 17:36<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ja, das weiss ich selbst...ich hab da wirklich total große probleme bei... <br /> <br />könnten wir deshalb das mal zusammen machen, wenigstens für eine <br /> <br />komponente...? <img src="images/smiles/help.gif" alt="Hilfe" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 17:28<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Du wirst doch wohl ableiten können... Produktregel, Kettenregel usw. <br />Wozu auch immer du diese Aufgabe für brauchst: Du solltest diese Grundlagen dringend nachholen, sonst kann es nichts werden. <br /> <br />Ableitung ist nicht überall die Variable mit 1 zu ersetzen.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 17:19<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">also, erst einmal vielen dank! Aber ich bin wirklich eine absolute niete in so etwas...aber ich probiere es mal...wäre es so richtig... <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_x E_x = \frac{\partial}{\partial x} \left( E_0 \cdot \frac{x}{\sqrt{x^2+y^2+z^2}} \right)= \left ( E_0 \cdot \frac{1}{\sqrt{1^2+y^2+z^2}} \right)"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_y E_y = \frac{\partial}{\partial y} \left( E_0 \cdot \frac{y}{\sqrt{x^2+y^2+z^2}} \right)= \left ( E_0 \cdot \frac{1}{\sqrt{x^2+1^2+z^2}} \right)"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_z E_z = \frac{\partial}{\partial z} \left( E_0 \cdot \frac{z}{\sqrt{x^2+y^2+z^2}} \right)= \left ( E_0 \cdot \frac{1}{\sqrt{x^2+y^2+1^2}} \right)"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 16:50<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Du musst doch nur eine Ableitung berechnen. Nehmen wir nur mal die x-Komponente: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_x E_x = \frac{\partial}{\partial x} \left( E_0 \cdot \frac{x}{\sqrt{x^2+y^2+z^2}} \right)= \dots"> <br /> <br />Weiter gehts mit <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_y E_y = \frac{\partial}{\partial y} \left( E_0 \cdot \frac{y}{\sqrt{x^2+y^2+z^2}} \right)= \dots"> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_z E_z = \dots"> <br /> <br />Dann: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\nabla \cdot \vec E = \partial_x E_x + \dots"> <br /> <br />und zuletzt musst du nur nach die Divergenz wieder durch <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r"> ausdrücken. <br /> <br /><span style="font-style: italic">Alternativ:</span> <br />Falls dich das nicht noch mehr verwirren sollte - aber die Aufgabe ist prädestiniert dafür mit der Divergenz in Kugelkoordinaten zu rechnen.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 16:41<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">naja, es ist so, dass ich ganz allgemein schwierigkeiten damit habe, <br /> <br />daher kann ich es wirklich nicht allein berechnen... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 15:55<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Einverstanden. Kannst du nun die Divergenz berechnen ?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 15:45<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">achso, also wäre <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r=\sqrt{x²+y²+z²}"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 15:42<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Nein, <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r"> ist ein Skalar, genauer der Betrag des Vektors <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec r"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 15:27<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">r wäre doch dann <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r=(x,y,z)"> oder... <img src="images/smiles/kopfkratz.gif" alt="grübelnd" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 14:49<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ist doch eigentlich ganz einfach: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec r = \begin{pmatrix} x \\ y \\ z \end{pmatrix} "> <br /> <br />Was ist dann <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r"> ?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 14:41<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">ja, dort liegt wahrscheinlich auch mein problem...aber ich weiss nicht, wie ich es umschreiben und dann damit rechnen soll...</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 14:39<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Schreib mal <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec r"> und <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r"> um mit x,y und z. Wahrscheinlich liegt dort dein Problem.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 14:01<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">naja ich weiss, dass die divergenz eines vektorfeldes folgendermaßen <br /> <br />definiert ist. Aber ich weiss nicht wirklich, wie ich nun damit die divergenz <br /> <br />zu meinem vektorfeld berechnen soll... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>mzh</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 22. Apr 2011 12:05<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">arbeitest du evtl. gerade an Aufgabe 1.62 in Griffith? Ich bin da auch gerade dran..</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>pressure</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 21. Apr 2011 20:11<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Wo liegt dein Problem : <br /> <br />-Weiß du wie die Divergenz eines Vektorfeldes definiert ist ? <br />-Kommst du nicht mir <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec r"> und <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?r"> klar ? <br /> <br />Um dir zu helfen, brauchen wir schon einen Hinweis.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Ricky</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 21. Apr 2011 19:45<span class="gen"> </span> Titel: Divergenz von Vektorfeldern</span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Hallo zusammen, <br /> <br />ich habe enorme probleme bei folgender aufgabe. Daher hoffe ich <br /> <br />wirklich sehr darauf, dass ihr mir helfen könnt... <img src="images/smiles/help.gif" alt="Hilfe" border="0" /> <img src="images/smiles/prost.gif" alt="Prost" border="0" /> <img src="images/smiles/prost.gif" alt="Prost" border="0" /></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> </table>
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