פוטנציאל חשמלי, קיבול וקבלים

✦ בנוי על ידי פהד גאנם ✦

V = k·qr   |   V = V1 + V2   |   W = q0·(VB − VA)
+6.0 nC
−6.0 nC
0.80 m
0.55 m
0.45 m
2.0 nC
0
0
0
0
0
0
0
0
0
0
0

V(A) = k·qrA = 8.99·10⁹ · 5.0·10⁻⁹0.30 = 44.950.30 = 149.8 V
V(B) = k·qrB = 44.950.50 = 89.9 V
ΔV = V(B) − V(A) = 89.9 − 149.8 = −59.9 V
W = q0·ΔV = 2.0·10⁻⁹ · (−59.9) = −1.2·10⁻⁷ J

E = Vd   |   qV = mv²2   |   v = √2qVm   |   1 eV = 1.602×10⁻¹⁹ J
500 V
0.050 m
0
0
0
0
0
0
0
0

E_k = qV = 1.602×10⁻¹⁹ · 500 = 8.01×10⁻¹⁷ J
E_k = 8.01×10⁻¹⁷ J1.602×10⁻¹⁹ J = 500 eV
v = √2E_km = √2 · 8.01×10⁻¹⁷9.109×10⁻³¹ = √1.759×10¹⁴ = 1.33×10⁷ m/s
E = Vd = 500 V0.050 m = 1.00×10⁴ V/m

v₀ = √2·e·Vm   |   a = e·Um·d   |   Y = U·L·(L + 2·D)4·d·V
1000 V
100 V
0.060 m
0.020 m
0.20 m
0
0
0
0
0
0
0

e·V = ½·m·v₀² v₀ = √2·e·Vm = √2 · 1.602·10⁻¹⁹ · 10009.109·10⁻³¹ = 1.875·10⁷ m/s
t = Lv₀ = 0.0601.875·10⁷ = 3.20·10⁻⁹ s = 3.20 ns
E = Ud = 1000.020 = 5.00·10³ V/m a = e·Em = 1.602·10⁻¹⁹ · 5.00·10³9.109·10⁻³¹ = 8.79·10¹⁴ m/s²
y₁ = ½·a·t² = ½ · 8.79·10¹⁴ · (3.20·10⁻⁹)² = 4.50·10⁻³ m = 4.5 mm y₁ = U·L²4·d·V = 100 · 0.060²4 · 0.020 · 1000 = 4.5 mm

C = QV = εr·ε₀·Ad   |   Q = C·V   |   U = ½CV²
100 cm²
2.0 mm
10.0 V
1.0
0
0
0
0
0
0

A = 150 cm² = 1.5·10⁻² m²    d = 2.5 mm = 2.5·10⁻³ m
C = εr·ε₀·Ad = 3.5 · 8.85·10⁻¹² · 1.5·10⁻²2.5·10⁻³ = 1.86·10⁻¹⁰ F = 186 pF
Q = C·V = 1.86·10⁻¹⁰ · 12 = 2.23·10⁻⁹ C = 2.23 nC
U = ½CV² = 0.5 · 1.86·10⁻¹⁰ · 12² = 1.34·10⁻⁸ J = 13.4 nJ

Cpar = C1 + C2 + C3   |   Cser = 11C1 + 1C2 + 1C3   |   E = 12 · C · V²
12.0 V
4 µF
12 µF
6 µF
0
0
0
0
0
0
0
0
0
0
0
0

C = C1 + C2 = 4.0 + 12 = 16 µF
Q = C · V = 16 · 12 = 192 µC E = 12 · C · V² = 12 · 16·10⁻⁶ · 144 = 1.152·10⁻³ J = 1.152 mJ
C = 114.0 + 112 = 4.0 · 124.0 + 12 = 4816 = 3.0 µF
Q = C · V = 3.0 · 12 = 36 µC E = 12 · C · V² = 12 · 3.0·10⁻⁶ · 144 = 0.216·10⁻³ J = 0.216 mJ V1 = QC1 = 364.0 = 9.0 V    V2 = QC2 = 3612 = 3.0 V    V1 + V2 = 12 V C = QV = 3612 = 3.0 µF < 4.0 µF

F = Q²2·ε₀·A = ½·Q·E
Wext = ΔU − V·ΔQ
Q = const :  Wext = ΔU = F·Δd
V = const :  Wext = ½·V²·(C₁ − C₂)
2.0 mm
12.0 V
100 cm²
0
0
0
0
0
0
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C₁ = ε₀·Ad₁ = 8.85·10⁻¹² · 10⁻²2·10⁻³ = 44.25 pF Q = C₁·V = 44.25·10⁻¹² · 12 = 5.31·10⁻¹⁰ C
U₁ = Q²2·C₁ = 3.19·10⁻⁹ J    C₂ = 22.125 pF    U₂ = Q²2·C₂ = 6.37·10⁻⁹ J W_ext = ΔU = U₂ − U₁ = 3.19·10⁻⁹ J ≈ 3.19 nJ
F = Q²2·ε₀·A = (5.31·10⁻¹⁰)²2 · 8.85·10⁻¹² · 10⁻² = 1.59·10⁻⁶ N W_ext = F·Δd = 1.59·10⁻⁶ · 2·10⁻³ = 3.19·10⁻⁹ J ✓
W_ext = ½·V²·(C₁ − C₂) = 0.5 · 12² · 22.125·10⁻¹² = 1.59·10⁻⁹ J ≈ 1.59 nJ ΔU = −1.59 nJ    V·ΔQ = −3.19 nJ    W_ext = ΔU − V·ΔQ = 1.59 nJ ✓
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