R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
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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 />
max<br />
Putting the derivative to zero ......<br />
⎛ R<br />
⎜<br />
⎝ R<br />
R<br />
2<br />
1<br />
⎞<br />
⎟<br />
⎠<br />
opt<br />
= e =<br />
2<br />
1, opt 2<br />
∂E<br />
⎛R<br />
∂ ⎜<br />
⎝ R<br />
2,718<br />
Optimized maximum el. field strength:<br />
R<br />
= = 0,368⋅R<br />
Emax, opt<br />
e<br />
2<br />
1<br />
⎞<br />
⎟<br />
⎠<br />
U U e⋅U<br />
= = =<br />
⎛ R ⎞ R<br />
2<br />
1, opt<br />
R2<br />
R1, opt<br />
ln ⎜ ⎟<br />
⎝ R ⎠<br />
1 opt<br />
<strong>Fachgebiet</strong><br />
<strong>Hochspannungstechnik</strong><br />
High-Voltage Technology / Chapter 6 - 45 -