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v<br />

BC<br />

ρ<br />

B<br />

ρ B D<br />

= ln<br />

2πε r<br />

BC<br />

B<br />

v<br />

BC ρ<br />

c<br />

ρC<br />

r<br />

= ln<br />

2πε D<br />

C<br />

BC<br />

Jadi<br />

vBC<br />

1 ⎛ D<br />

⎜ AC<br />

=<br />

ρ A ln<br />

2πε<br />

⎝ DAB<br />

DBC<br />

+ ρ B ln<br />

rB<br />

rC<br />

⎞<br />

+ ρC<br />

ln ⎟<br />

D<br />

BC ⎠<br />

(10.25)<br />

Beda Potensial Empat Konduktor Bermuatan. Empat konduktor<br />

bermuatan terlihat pada Gb.10.8:<br />

A,<br />

r<br />

A<br />

, ρ<br />

A<br />

B,<br />

Gb. 10.8. <strong>Sistem</strong> empat konduktor.<br />

Kita akan meninjau sistem empat konduktor seperti terlihat pada<br />

gambar di atas dengan ketentuan konservasi muatan, yaitu<br />

1 ⎛ D<br />

⎜ A DB<br />

v A =<br />

ρ A ln + ρ B ln<br />

2πε<br />

⎝ rA<br />

DAB<br />

1 ⎛ D<br />

⎜ A DB<br />

vB<br />

=<br />

ρ A ln + ρ B ln<br />

2πε<br />

⎝ DAB<br />

rB<br />

1 ⎛ D<br />

⎜ A DB<br />

vC<br />

=<br />

ρ A ln + ρ B ln<br />

2πε<br />

⎝ DAC<br />

DBC<br />

1 ⎛ D<br />

⎜ A<br />

v = ln<br />

2<br />

ρ A<br />

πε ⎝ D A<br />

ρ A + ρ A + ρ A + ρ A = 0<br />

(10.26)<br />

DB<br />

+ ρ B ln<br />

DB<br />

DC<br />

+ ρC<br />

ln<br />

DAC<br />

DC<br />

+ ρC<br />

ln<br />

DBC<br />

DC<br />

+ ρC<br />

ln<br />

rC<br />

DC<br />

+ ρC<br />

ln<br />

DC<br />

Jika kita terapkan relasi konservasi muatan (10.26)<br />

r<br />

r<br />

⎞<br />

+ ρ ln ⎟<br />

D<br />

A ⎠<br />

r<br />

⎞<br />

+ ρ ln ⎟<br />

D<br />

B ⎠<br />

r<br />

⎞<br />

+ ρ ln ⎟<br />

D<br />

C ⎠<br />

D<br />

⎞<br />

+ ρ ln ⎟<br />

= 0<br />

D<br />

⎠<br />

ρa + ρb<br />

+ ρc<br />

+ ρn<br />

= 0 atau ρ n = −( ρa<br />

+ ρb<br />

+ ρc<br />

)<br />

maka ρ akan ter-eliminasi dari persamaan (10.27)<br />

B<br />

, ρ<br />

B<br />

C, r<br />

C<br />

, ρ<br />

C<br />

N, r<br />

<br />

, ρ<br />

<br />

(10.27)<br />

234 Sudaryatno Sudirham, Analisis <strong>Rangkaian</strong> <strong>Sistem</strong> Tenaga

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