Cinque cariche puntiformi di valori rispettivamente Q
A
= 120 nC, Q
B
= +250 nC, Q
C
= -560 nC, Q
D
= 340 nC, Q
E
= -120 nC
occupano, nel vuoto, i vertici di un poligono come in figura. Determina l’energia elettrostatica del sistema di cariche.
E
TOT
=
E
BA
+
(
E
CA
+
E
CB
)
+
(
E
DA
+
E
DB
+
E
DC
)
+
(
E
EA
+
E
EB
+
E
EC
+
E
ED
)
=
=
k
(
Q
A
Q
B
d
AB
+
Q
C
Q
A
d
CA
+
Q
C
Q
B
d
CB
+
Q
D
Q
A
d
DA
+
Q
D
Q
B
d
DB
+
Q
D
Q
C
d
DC
+
Q
E
Q
A
d
EA
+
Q
E
Q
B
d
EB
+
Q
E
Q
C
d
EC
+
Q
E
Q
D
d
ED
)
=
=
8.9
⋅
(
120
⋅
250
29
−
560
⋅
120
11
−
560
⋅
250
194
+
340
⋅
120
80
+
340
⋅
250
181
−
340
⋅
560
25
−
120
⋅
120
17
−
120
⋅
250
61
+
120
⋅
560
50
−
120
⋅
340
41
)
⋅
10
−
6
≈
−
0.374
J
E_TOT= E_BA+(E_CA+E_CB)+(E_DA+E_DB+E_DC)+(E_EA+E_EB+E_EC+E_ED)"=" newline "="k left ( {Q_A Q_B} over {d_AB} + {Q_C Q_A} over {d_CA}+ {Q_C Q_B} over {d_CB}+ {Q_D Q_A} over {d_DA}+ {Q_D Q_B} over {d_DB}+ {Q_D Q_C} over {d_DC}+ {Q_E Q_A} over {d_EA}+ {Q_E Q_B} over {d_EB}+ {Q_E Q_C} over {d_EC}+ {Q_E Q_D} over {d_ED}right ) "=" newline "="8.9 cdot left ( {120 cdot 250} over {sqrt 29} - {560 cdot 120} over {11}- {560 cdot 250} over {sqrt 194}+ {340 cdot 120} over {sqrt 80}+ {340 cdot 250} over {sqrt 181} -{340 cdot 560} over {sqrt 25}- {120 cdot 120} over {sqrt 17}- {120 cdot 250} over {sqrt 61}+ {120 cdot 560} over {sqrt 50}- {120 cdot 340} over {sqrt 41} right )cdot 10^-6 approx -0.374 ~ J
