R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
R - Fachgebiet Hochspannungstechnik
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Analytical Solution of Gauss's Law<br />
2 nd step<br />
Evaluating the voltage difference by integration<br />
of the electric field strength along the path<br />
1<br />
U<br />
21<br />
2<br />
ds<br />
= ∫ E Enveloping<br />
R<br />
R<br />
2 2<br />
2<br />
Q 1 Q ⎡ 1⎤<br />
Q ⎛ 1 1 ⎞ Q R − R<br />
URR<br />
= E()<br />
r dr dr<br />
1 2 ∫ = ∫ = ⋅ − = ⋅ − = ⋅<br />
R<br />
⎣ ⎦ ⎝ ⎠<br />
1 1<br />
R<br />
2 1<br />
2<br />
4πε r 4πε ⎢ r⎥ ⎜ ⎟<br />
R<br />
4πε R1 R2 4πε<br />
R<br />
R<br />
1⋅<br />
R2<br />
1<br />
R1⋅<br />
R2<br />
Q = 4πεU ⋅ R − R<br />
2 1<br />
surface A<br />
<strong>Fachgebiet</strong><br />
<strong>Hochspannungstechnik</strong><br />
High-Voltage Technology / Chapter 6 - 21 -