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R - Fachgebiet Hochspannungstechnik

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Analytical Solution of Gauss's Law<br />

1 st step<br />

Resolution of Gauss's Law<br />

∫∫<br />

D d A<br />

A<br />

= Q<br />

to the absolute value of D<br />

∫∫<br />

A<br />

DA<br />

∫∫<br />

2<br />

d = D() r dA= D() r ⋅ A() r = D()4<br />

r ⋅ π r = Q<br />

A<br />

Dr () =<br />

Er () =<br />

Q<br />

2<br />

4π<br />

r<br />

Q<br />

4πε<br />

r<br />

2<br />

same procedure as for sphere in free space<br />

<strong>Fachgebiet</strong><br />

<strong>Hochspannungstechnik</strong><br />

High-Voltage Technology / Chapter 6 - 20 -

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