פתרון בגרות · חשמל

✦ בנוי על ידי פהד גאנם ✦

r = 0.9 m  |  m = 0.01 kg  |  v₀ = 2 m/s
k = 9·10⁹ N·m²/C²  |  e = 1.6·10⁻¹⁹ C
2.00
44.4
2.83
1.25

Fe = (−e)·E  ⟸ 
qA + qB + qC = 0

N = m·g
FC = k·|qA|·|qC|

k·q² = m·v₀²r
q² = m·v₀²·rk = 0.01 · 2² · 0.99·10⁹ = 0.0369·10⁹ = 4·10⁻¹² C²
q = 4·10⁻¹² = 2·10⁻⁶ C = 2 μC
F = 9·10⁹ · (2·10⁻⁶)²0.9² = 4.44·10⁻² N  ,  m·v₀²r = 0.01 · 40.9 = 4.44·10⁻² N

Δn = |q|e = 2·10⁻⁶1.6·10⁻¹⁹ = 1.25·10¹³

k·q² = m·v₀²r  ⟸ 

a = 0.6 m  |  q₁ = q₂ = +40·10⁻⁹ C  |  k = 9·10⁹ N·m²/C²
q₃ = −40 μC  |  xK = 6 cm  |  a3 = 2 m/s²
40 nC
1732
1200
2400
150
6.0

E₁ = E₂ = k·q = 9·10⁹ · 40·10⁻⁹0.6² = 3600.36 = 1000 V/m
E = 2 · E₁ · cos30° = 2 · 1000 · 0.866 = 1732 V/m E = 3 · 1000 = 1.73·10³ V/m

V₁ = V₂ = k·qa = 9·10⁹ · 40·10⁻⁹0.6 = 3600.6 = 600 V
V = V₁ + V₂ = 600 + 600 = 1200 V

E1 = E2 = k·q  ,  r = a2 = 0.3 m Etot = E1 − E2 = 0  , 
V = 2 · k·qa2 = 2 · 3600.3 = 2400 V

Ex = − ΔVΔx
E = − 6 − 00.02 − 0 = − 60.02 = −300 V/m
E = − 00.02 = 0
E = − 0 − 60.08 − 0.04 = + 60.04 = +150 V/m

E(K) = +150 V/m  ⟸ 
F = q₃ · E = (−40·10⁻⁶) · (+150) = −6·10⁻³ N

|F| = |q₃| · E = 40·10⁻⁶ · 150 = 6·10⁻³ N
m = |F|a = 6·10⁻³2 = 3·10⁻³ kg

I (A) : 0.5   1.0   1.5   2.0   2.5
V (V) : 4.9   3.9   3.2   2.0   0.8
40 %
4.00
1.00
4.00
6.00
2.00

I = εr + RMK

(0.5 , 4.9)   (1.0 , 3.9)   (1.5 , 3.2)   (2.0 , 2.0)   (2.5 , 0.8)
V = −2.02 · I + 5.99
V = ε − I·r

V = ε − I·r
I = 0  ⟹  V = ε ε = 6.0 V
ε = V + I·r = 5.0 + 0.5 · 2.0 = 6.0 V

(I₁ , V₁) = (0.5 , 5.0)  ,  (I₂ , V₂) = (2.5 , 1.0)
= V₂ − V₁I₂ − I₁ = 1.0 − 5.02.5 − 0.5 = −4.02.0 = −2.0 Ω
r = 2.0 Ω

RMK = 0
I = εr + RMK = 6.02.0 + 0 = 3.0 A

R = VI =
R = 9.80   3.90   2.13   1.00   0.32 Ω
V = ε − I·r

I = 8.5 A  |  r = 10 cm  |  α = 37°  |  μ₀ = 4π·10⁻⁷ T·m/A
8.5 A
1.70
2.26
37
0.75

BI = μ₀·I2π·r
tan(α) = BIBE
tan(α) = μ₀·I2π·r·BE

BI = 4π·10⁻⁷ · 8.52π · 0.10 = 2·10⁻⁷ · 8.50.10 = 1.7·10⁻⁵ T
BE = BItan(37°) = 1.7·10⁻⁵0.754 = 2.26·10⁻⁵ T

tan(55°) = 1.43 > 1  ⟹  BI > BE

B = 1 T  |  v = 3.6·10⁶ m/s  |  m = 6.67·10⁻²⁷ kg
PC = 15 cm  |  QF = 15 cm  |  e = 1.6·10⁻¹⁹ C
15.0
1.60
0.0
0.00
0

F = q · v × B

:  • 
:  × 
:  × 

Δx = 15 cm  ,  Δy = 15 cm  ⟹  r = 0.15 m
r = m·v|q|·B  ⟹  |q| = m·vr·B |q| = 6.67·10⁻²⁷ · 3.6·10⁶0.15 · 1 = 2.40·10⁻²⁰0.15 = 1.6·10⁻¹⁹ C

W = 0  ⟹  ΔEk = 0  ⟹  v =

90° + 180° + 90° = 360°
S = 2π·r = 2π · 0.15 = 0.942 m
t = Sv = 0.9423.6·10⁶ = 2.6·10⁻⁷ s
T = 2π·m|q|·B = 2π · 6.67·10⁻²⁷1.6·10⁻¹⁹ · 1 = 2.6·10⁻⁷ s

F = q · v × B

K = 0.02  |  R = 0.04 Ω  |  a = 2 m/s²
B(x) = B0,x − K·x  |  x = ½·a·t²
2.0 m/s²
0.020 T/m
0.00
0.0
5.00
10.0
0.00

B(x) = B0,x − K·x
K = B0,x − B(x)x  ⟹  [K] = Tm

Φ = B · A
ε = − ΔΦΔt  ,  I = εR

x(t) = 12·a·t²
B(t) = B0,x − K · 12·a·t²
Φ(t) = A · B(t) = A·B0,x12·A·K·a·t²

|ε| = ΔΦΔt = A·K·a·t
I(t) = |ε|R = A·K·aR · t

= 0.6 − 00.3 − 0 = 2.0 mA/s = 2·10⁻³ A/s
A·K·aR = 2·10⁻³  ⟹  A = 2·10⁻³ · RK · a
A = 2·10⁻³ · 0.040.02 · 2 = 8·10⁻⁵0.04 = 2·10⁻³

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