פתרון בגרות חשמל — שאלון 36371

1/r² (m⁻²) | 20 | 25 | 32 | 42 | 57 | 80 | 95
E (N/C) | 3000 | 3200 | 3550 | 4100 | 4800 | 5950 | 6700
m = 0.2 g · E = 5700 N/C · α = 14° · k = 9·10⁹ N·m²/C² · g = 10 m/s²

15.0 cm

0.150

44.44

4188

366

193

4.96

T·sinα = q₁E T·cosα = mg

tanα = T·sinαT·cosα = q₁Emg

E = mg·tanαq₁

q₁ = mg·tanαE = 2·10⁻³ · 0.24935700 = 8.7·10⁻⁸ C

F_c = kq₁q₂r²

T·sinβ = q₁E − kq₁q₂r²

T·cosβ = mg

tanβ = q₁E − kq₁q₂r²mg

mg·tanβ = q₁E − kq₁q₂r² q₁E = kq₁q₂r² + mg·tanβ E = kq₂r² + mgq₁·tanβ

E = k·q₂ · 1r² + mgq₁·tanβ

k·q₂ = ΔEΔ(1/r²) = 198440 = 49.6 N·m²/C

mgq₁·tanβ = 1984 N/C q₂ = k·q₂k = 49.69·10⁹ = 5.5·10⁻⁹ C

tanβ = 1984 · 8.75·10⁻⁸2·10⁻³ = 0.0868 β = 5°

1/r² (m⁻²) | 20 | 25 | 32 | 42 | 57 | 80 | 95
E נמדד (N/C) | 3000 | 3200 | 3550 | 4100 | 4800 | 5950 | 6700
E מודל (N/C) | 2976 | 3224 | 3571 | 4067 | 4812 | 5953 | 6697

F₁ = q₁E − F_c , F_c = kq₁q₂r²

F₂ = q₂E + F_c

tanθ₁ = F₁mg , tanθ₂ = F₂mg q₁E − F_c = q₂E + F_c

(q₁ − q₂)E = 2F_c > 0 → q₁ > q₂

q₂ = q₁ − 2F_cE

Q = 6·10⁻¹⁰ C · d = 6 cm · V_B = 91 V
e⁺ : q_e = +1.6·10⁻¹⁹ C · m_e = 9.11·10⁻³¹ kg · v_O = 5.2·10⁶ m/s
k = 9·10⁹ N·m²/C²

2.2·10⁻¹⁰ C

−69°

2.20

123

91

−41

6.19

116

E_Q = kQd²

E_q = kqd²

E_O = kQd² − kqd² = kQ − qd²

E_O = 9·10⁹ · (6·10⁻¹⁰ − 2.2·10⁻¹⁰)0.06² = 950 N/C

V = kQr_Q + kqr_q

y₀ = d√q − √Q√q + √Q = −1.5 cm

V = kQr_Q + kqr_q

91 = 9·10⁹ · 6·10⁻¹⁰0.157 + 9·10⁹ · q0.037 91 = 34.4 + 2.43·10¹¹ · q q = 56.62.43·10¹¹ = 2.3·10⁻¹⁰ C

V (V)      | 91   | 72   | 54   | 36
y (cm)     | −9.7 | −11.0 | −13.6 | −19.2
r_Q (m)   | 0.157 | 0.170 | 0.196 | 0.252
r_q (m)   | 0.037 | 0.050 | 0.076 | 0.132
q (10⁻¹⁰ C) | 2.33 | 2.24 | 2.23 | 2.14

V_O = kQ + qd = 9·10⁹ · 8.2·10⁻¹⁰0.06 = 123 V

V_B = 91 V

½mv_B² = ½mv_O² + q_e(V_O − V_B)

½mv_O² = ½ · 9.11·10⁻³¹ · (5.2·10⁶)² = 1.232·10⁻¹⁷ J q_e(V_O − V_B) = 1.6·10⁻¹⁹ · 32 = 5.12·10⁻¹⁸ J ½mv_B² = 1.744·10⁻¹⁷ J

v_B = √2 · 1.744·10⁻¹⁷9.11·10⁻³¹ = 6.2·10⁶ m/s

a = q_eEm

ε = 12 V · I = 1.25 A · V₁ = 8 V
L = 40 cm · V₂ = 6 V · ההתנגדות הפנימית זניחה

2

40

1.25

8.00

6.00

0.625

6.4

V_מוטות = ε − V₁ = 12 − 8 = 4 V

R_שקול = V_מוטותI = 41.25 = 3.2 Ω

1R_שקול = 1R_x + 1R_x = 2R_x → R_x = 2R_שקול R_x = 2 · 3.2 = 6.4 Ω

R = V₁I = 81.25 = 6.4 Ω

ε = I·(R + R_שקול) = 1.25 · (6.4 + 3.2) = 1.25 · 9.6 = 12 V ✓

I_מוט = I2 = 1.252 = 0.625 A

R_MP = V₂I_מוט = 60.625 = 9.6 Ω

λ = R_MPL = 9.60.40 = 24 Ω/m

אורך המוט = R_xλ = 6.424 ≈ 0.27 m

1R_שקול = n · 1R_x → R_שקול = R_xn

I = εR + R_xn = nεnR + R_x

I = 2 · 122 · 6.4 + 6.4 = 2419.2 = 1.25 A ✓

R_שקול = R_xn ↓ ⇒ I ↑

V₁ = I · R , R קבוע ⇒ V₁ ↑

V_מוטות = ε − V₁ ↓ ⇒ V₂ ↓

נקודה | M₁ | M₂ | M₃ | M₄ | M₅
I (A) | 0.5 | 1.0 | 2.0 | 3.0 | 4.0
P (W) | 3.5 | 6.0 | 8.0 | 6.0 | 0.0

2.00

2.00

4.00

8.00

50.0

I = εR + r , R ↑ ⇒ I ↓

V = ε − I·r , I ↓ ⇒ V ↑

P = I²R → R = PI² = 3.50.5² = 3.50.25 = 14 Ω

P = εI − I²r

P = 0 → εI = I²r → I_אפס = εr = 4 A I_קודקוד = ε2r = 2 A , P_מרבי = ε²4r = 8 W

r = P_מרביI_קודקוד² = 84 = 2 Ω ε = I_אפס · r = 4 · 2 = 8 V

P_מבוזבז = I²r

M₂: P_מבוזבז = 1² · 2 = 2 W M₄: P_מבוזבז = 3² · 2 = 18 W

P_M₄P_M₂ = 182 = 9

V = ε − I·r − I·R = ε − 0 − 0 = ε

v₀ = 2·10⁶ m/s · q = 1.6·10⁻¹⁹ C
B₁ = 0.05 T · t₁ = 3.279·10⁻⁷ s · KP = 62.6 cm

50

41.7

20.9

1.67

0.100

1.0

F = q · v × B

t₁ = T4 → T = 4t₁ = 4 · 3.279·10⁻⁷ = 1.3116·10⁻⁶ s

qvB = mv²R → R = mvqB T = 2πRv = 2πmqB

m = qB₁T2π = 1.6·10⁻¹⁹ · 0.05 · 1.3116·10⁻⁶2π = 1.67·10⁻²⁷ kg

R₁ = mv₀qB₁ = 1.67·10⁻²⁷ · 2·10⁶1.6·10⁻¹⁹ · 0.05 = 0.4175 m ≈ 41.7 cm

KP = R₁ + R₂ → R₂ = KP − R₁ = 62.6 − 41.7 = 20.9 cm

R₂ = mv₀qB₂ → B₂ = mv₀qR₂ = 1.67·10⁻²⁷ · 2·10⁶1.6·10⁻¹⁹ · 0.209 = 0.1 T B₂ = B₁ · R₁R₂ = 0.05 · 41.720.9 ≈ 0.1 T

F_חשמלי = F_מגנטי → qE = qv₀B₁

E = v₀ · B₁ = 2·10⁶ · 0.05 = 1·10⁵ V/m

i (A) | 1.0 | 3.0 | 5.0 | 7.0 | 9.0
T (N) | 0.090 | 0.075 | 0.045 | 0.035 | 0.010

5.0

0.045

0.100

0.202

20.2

0.200

F = i · L × B

2T + BiL = mg

T = mg − BiL2 = mg2 − BL2·i

T = mg2 − BL2·i מול y = חיתוך + שיפוע · x

mg2 = 0.101 → m = 2 · 0.10110 = 0.0202 kg ≈ 20 גרם

שיפוע = ΔTΔi = 0.010 − 0.0909.0 − 1.0 = −0.0808.0 = −0.010 N/A −BL2 = −0.010 → B = 2 · 0.0100.10 = 0.2 T

F = B·i·L·sinθ , θ = 0 → sinθ = 0 → F = 0

2T = mg → T = mg2 ≈ 0.10 N

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