R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Analytical Solution of Gauss's Law<br />
5 th step<br />
Evaluation of maximum electric field strength E max<br />
Optimization (e.g. minimization of electrical field strength E max )<br />
E<br />
∂Emax<br />
Putting the derivative to zero ......<br />
⎛R<br />
⎞<br />
2<br />
∂ ⎜ ⎟<br />
⎝ R1<br />
⎠<br />
U U R<br />
= E = = ⋅<br />
R<br />
R1<br />
⋅ln<br />
R<br />
ln<br />
R<br />
max 1<br />
R<br />
R<br />
R<br />
2 1<br />
2 2 2<br />
1 1<br />
u<br />
v<br />
What is needed?<br />
' ' '<br />
⎛u⎞ uv − uv<br />
Quotientenregel : ⎜ ⎟ =<br />
2<br />
⎝v<br />
⎠ v<br />
d ( ln x)=<br />
1<br />
dx<br />
x<br />
<strong>Fachgebiet</strong><br />
<strong>Hochspannungstechnik</strong><br />
High-Voltage Technology / Chapter 6 - 44 -