מגנטיות ואלקטרומגנטיות — 33.9001 · תורת החשמל לטכנאים

0.40 T

2.0 A

50

10 cm

6 cm

0°

60 cm²

4.00 N

6.00 cm

0.240 N·m

0.600 A·m²

90°

0.00 N

F = N·B·I·a = 200 · 0.5 · 3 · 0.12 = 36 N

A = a·b = 0.12 · 0.08 = 9.6·10⁻³ m²

M_max = F·b = 36 · 0.08 = 2.88 N·m M_max = N·B·I·A = 200 · 0.5 · 3 · 9.6·10⁻³ = 2.88 N·m

M = M_max·cos60° = 2.88 · 0.5 = 1.44 N·m

μ₀ = 4π·10⁻⁷ H/m | B = μ·H = μ₀·μ_r·H | μ_r = μμ₀ = Bμ₀·H | χ = μ_r − 1 | J = χ·H

200 A/m

5000

200 A/m

5000

6.28e−3 H/m

5.027 T

1.01 mT

4999

4.0e6 A/m

×5000

μ = μ₀·μ_r = 4π·10⁻⁷ · 2000 = 2.513·10⁻³ H/m

B = μ·H = 2.513·10⁻³ · 500 = 1.257 T

Φ = B·A = 1.257 · 4·10⁻⁴ = 5.03·10⁻⁴ Wb = 0.503 mWb

B₀ = μ₀·H = 4π·10⁻⁷ · 500 = 6.28·10⁻⁴ T = 0.628 mT

B_r = B(H=0) | H_c = H(B=0) | w_h = ∮H·dB | P_h = w_h·f·V | μ_r = Bμ₀·H

180 A/m

50 Hz

1500 cm³

0 A/m

0.00 T

1.05 T

30 A/m

—

1.90 T

— J/m³

— W

V = 1500 cm³ = 1.5·10⁻³ m³

W = w_h·V = 480 · 1.5·10⁻³ = 0.72 J

P_h = W·f = 0.72 · 50 = 36 W

P_h = 0.72 · 400 = 288 W

2.0 A

400

8 cm

50 %

800 A

0.503 m

1591 A/m

2.00 mT

800 A·t

8.00 cm

l = 2π·r = 2π · 0.1 = 0.6283 m

ΣI = N·I = 500 · 1.5 = 750 A H = N·Il = 7500.6283 = 1194 A/m

B = μ₀·H = 4π·10⁻⁷ · 1194 = 1.50·10⁻³ T = 1.5 mT

B = μ₀·μ_r·H = 4π·10⁻⁷ · 1200 · 1194 = 1.80 T

F = N·I | R_m = lμ₀·μ_r·A | Φ = FR_m | B = ΦA | H = Fl

300

0.8 A

40 cm

6 cm²

1500

240 A·t

3.54e5 A/Wb

0.679 mWb

1.131 T

600 A/m

1.88e−3 H/m

254 mH

2.83 µWb/A

F = N·I = 300 · 0.8 = 240 A·t

R_m = lμ₀·μ_r·A = 0.44π·10⁻⁷ · 1500 · 6·10⁻⁴ = 3.537·10⁵ A/Wb

Φ = FR_m = 2403.537·10⁵ = 6.786·10⁻⁴ Wb = 0.679 mWb

B = ΦA = 6.786·10⁻⁴6·10⁻⁴ = 1.131 T

H = Fl = 2400.4 = 600 A/m B = μ₀·μ_r·H = 4π·10⁻⁷ · 1500 · 600 = 1.131 T

R_m,Fe = l_Feμ₀·μ_r·A | R_m,g = l_gμ₀·A | R_m = R_m,Fe + R_m,g | N·I = H_Fe·l_Fe + H_g·l_g

2.0 mm

1500 A·t

50 cm

8 cm²

2000

2.48e5 A/Wb

1.99e6 A/Wb

2.24e6 A/Wb

0.670 mWb

0.838 T

333 A/m

6.67e5 A/m

89 %

l_Fe = 0.5 − 0.002 = 0.498 m R_m,Fe = 0.4984π·10⁻⁷ · 2000 · 8·10⁻⁴ = 2.477·10⁵ A/Wb

R_m,g = 0.0024π·10⁻⁷ · 8·10⁻⁴ = 1.989·10⁶ A/Wb

R_m = 2.477·10⁵ + 1.989·10⁶ = 2.237·10⁶ A/Wb Φ = 500 · 32.237·10⁶ = 6.705·10⁻⁴ Wb = 0.670 mWb

B = 6.705·10⁻⁴8·10⁻⁴ = 0.838 T R_m,gR_m = 1.989·10⁶2.237·10⁶ = 0.889 → 1334 A·t

Φ = Φ₁ + Φ₂ | R_m,12 = R_m1·R_m2R_m1 + R_m2 | R_m = R_m,c + R_m,12 | Φ₁ = Φ·R_m2R_m1 + R_m2

250 A·t

30 cm

45 cm

6 cm²

2000

6.63e4 A/Wb

1.99e5 A/Wb

2.98e5 A/Wb

1.19e5 A/Wb

1.86e5 A/Wb

1.346 mWb

0.808 mWb

0.538 mWb

1.122 T

1.346 T

R_m,c = 0.24π·10⁻⁷ · 2000 · 12·10⁻⁴ = 6.63·10⁴ A/Wb R_m1 = 0.34π·10⁻⁷ · 2000 · 6·10⁻⁴ = 1.989·10⁵ A/Wb R_m2 = 0.454π·10⁻⁷ · 2000 · 6·10⁻⁴ = 2.984·10⁵ A/Wb

R_m,12 = 1.989·10⁵ · 2.984·10⁵1.989·10⁵ + 2.984·10⁵ = 1.194·10⁵ A/Wb R_m = 6.63·10⁴ + 1.194·10⁵ = 1.857·10⁵ A/Wb

F = 500 · 0.5 = 250 A·t Φ = 2501.857·10⁵ = 1.346·10⁻³ Wb = 1.346 mWb

Φ₁ = 1.346 · 2.9841.989 + 2.984 = 0.808 mWb Φ₂ = 1.346 − 0.808 = 0.538 mWb

F = N·I | R_m = ℓμ₀·μ_r·A | Φ = FR_m | B = ΦA

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