פתרון בגרות · חשמל
✦ בנוי על ידי פהד גאנם ✦
العربية
☀ מצב בהיר
1
▾
✕
E (10⁴ V/m) | 5 | 10 | 15 | 20 | 25
a (m/s²) | −9.5 | −5.0 | −0.5 | +2.5 | +6.5
15
7.9
−13.1
−10.0
−1.20
F
E
= +qE
F
g
= −mg
ΣF = ma → qE − mg = ma
a =
qE − mg
m
=
q
m
E − g
a =
q
m
E − g מול y =
שיפוע
· x +
חיתוך
q
m
=
Δa
ΔE
=
6.5 − (−9.5)
25·10⁴ − 5·10⁴
=
16
20·10⁴
= 8.0·10⁻⁵
m/s²
V/m
=
C
kg
E = 0 → a =
q
m
·0 − g = −g = −10 m/s²
a(0) = a(15·10⁴) −
q
m
·15·10⁴ ≈ −0.5 − 12.0 ≈ −12.5 m/s²
F = k
q₁q₂
r²
, q₁q₂ > 0 →
דחייה
|F
קרוב
| > |F
רחוק
| →
שקול של משיכה
2
▾
✕
R₁ = 10 cm | R₂ = 60 cm | Q₂ = 10 nC | V(∞) = 0
V = 120 V | Δr = 5 cm | k = 9·10⁹ N·m²/C² | e = 1.6·10⁻¹⁹ C | m
p
= 1.673·10⁻²⁷ kg
10.0 nC
2.00
10.00
180.0
150.0
0.00
V = k
Q₁
r
r = R₁ + 0.05 = 0.10 + 0.05 = 0.15 m
Q₁ =
V·r
k
=
120 · 0.15
9·10⁹
=
18
9·10⁹
= 2·10⁻⁹ C
V
R
= k
Q₁
R₁
=
9·10⁹ · 2·10⁻⁹
0.10
=
18
0.10
= 180 V
½mv₀² + eV(∞) = ½mv² + eV
R
½mv₀² = eV
R
= 1.6·10⁻¹⁹ · 180 = 2.88·10⁻¹⁷ J
v₀ =
√
2eV
R
m
=
√
2 · 2.88·10⁻¹⁷
1.673·10⁻²⁷
=
√
3.443·10¹⁰
= 1.86·10⁵ m/s
Q₁′ + Q₂′ = Q₁ + Q₂ = 2 + 10 = 12 nC
k
Q₁′
R₁
= k
Q₂′
R₂
→
Q₁′
Q₂′
=
R₁
R₂
=
10
60
=
1
6
Q₁′ = 12 ·
R₁
R₁ + R₂
= 12 ·
10
70
= 1.71 nC
Q₂′ = 12 ·
R₂
R₁ + R₂
= 12 ·
60
70
= 10.29 nC
V′ =
9·10⁹ · 1.714·10⁻⁹
0.10
=
9·10⁹ · 10.286·10⁻⁹
0.60
= 154.3 V
ΔQ = Q₁ − Q₁′ = 2 − 1.714 = 0.286 nC = 2.86·10⁻¹⁰ C
n =
ΔQ
e
=
2.857·10⁻¹⁰
1.6·10⁻¹⁹
= 1.79·10⁹
3
▾
✕
V (V) | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0
I
B
(A) | 0.18 | 0.29 | 0.38 | 0.43 | 0.47 | 0.50 | 0.52 | 0.53
I
A
(A) | 0.10 | 0.20 | 0.30 | 0.40 | 0.50 | 0.60 | 0.70 | 0.80
0.46
3.5
2.30
2.30
0.46
0.46
0.46
4.60
5.0
R =
V
I
R
A
=
4.0
0.80
=
2.3
0.46
=
3.5
0.70
= 5 Ω
R
B
(0.5 V) =
0.5
0.20
= 2.5 Ω , R
B
(4.0 V) =
4.0
0.53
≈ 7.5 Ω
R =
ρ · ℓ
A
→ ρ =
R · A
ℓ
A = 0.45 mm² = 0.45 · 10⁻⁶ m²
ρ =
5 · 0.45 · 10⁻⁶
2
=
2.25 · 10⁻⁶
2
= 1.125 · 10⁻⁶ Ω·m
I
A
= I
B
, V
A
= V
B
V
A
= V
B
= 2.3 V , I = 0.46 A
I =
V
A
R
A
=
2.3
5
= 0.46 A
V
MN
= V
A
+ V
B
= 2.3 + 2.3 = 4.6 V
V
A
= V
B
= 3.5 V
I
A
=
V
R
A
=
3.5
5
= 0.70 A
I
B
= 0.52 A
I = I
A
+ I
B
= 0.70 + 0.52 = 1.22 A
ε = V
MN
+ I · r
ε = 4.6 + 0.46 · r , ε = 3.5 + 1.22 · r
4.6 + 0.46r = 3.5 + 1.22r → 1.1 = 0.76r
r =
1.1
0.76
≈ 1.45 Ω
ε = 4.6 + 0.46 · 1.45 = 4.6 + 0.67 ≈ 5.27 V
ε = 3.5 + 1.22 · 1.45 = 3.5 + 1.77 ≈ 5.27 V
R
שקול
=
R
A
· R
V
R
A
+ R
V
< R
A
4
▾
✕
x = ? | 0.16 | 0.265 | 0.50 | 0.625 | 0.78 | 0.81
R
MS
(Ω) | 2.0 | 4.7 | 9.6 | 13.0 | 16.3 | 17.6
10.0 Ω
1.99
0.50
19.9
39.7
6.9
85
ε = I·R
MS
+ I·r = I·(R
MS
+ r)
R
MS
+ r =
ε
I
→ R
MS
=
ε
I
− r
R
MS
= ε·
1
I
− r מול y =
שיפוע
· x +
חיתוך
x =
1
I
Ω
x
= V → x =
Ω
V
=
1
A
= A⁻¹
ε =
ΔR
MS
Δ
1
I
=
17.0 − 2.9
0.80 − 0.20
=
14.1
0.60
= 23.5 V
−r = 2.9 − 23.5 · 0.20 = 2.9 − 4.7 = −1.8 → r = 1.8 Ω
I =
ε
R
MS
+ r
=
23.5
10 + 1.8
=
23.5
11.8
= 1.99 A
P = I²·R
MS
= (1.99)² · 10 = 39.7 W ≈ 40 W
P =
ε²·R
MS
(R
MS
+ r)²
=
23.5² · 10
11.8²
=
5522
139.2
= 39.7 W
η =
P
חיצוני
P
כולל
=
I²·R
MS
ε·I
=
I·R
MS
ε
I·R
MS
= ε − I·r → η =
ε − I·r
ε
= 1 −
I·r
ε
P
r
= I²·r
5
▾
✕
B₁ = 0.02 T · v = 10⁶ m/s
e = 1.6·10⁻¹⁹ C · m
p
= 1.673·10⁻²⁷ kg
20 mT
10⁶ m/s
20 ·10³ V/m
40°
50°
3.20
0.52
3.28
305
F = q·v·B₁·sin90° = q·v·B₁
F = 1.6·10⁻¹⁹ · 10⁶ · 0.02 = 3.2·10⁻¹⁵ N
F = q·v ⨯ B₁
q·v·B₁ =
m·v²
R₁
R₁ =
m·v
q·B₁
=
1.673·10⁻²⁷ · 10⁶
1.6·10⁻¹⁹ · 0.02
=
1.673·10⁻²¹
3.2·10⁻²¹
= 0.52 m
T₁ =
2π·R₁
v
=
2π·m
q·B₁
=
2π · 1.673·10⁻²⁷
3.2·10⁻²¹
= 3.28·10⁻⁶ s
ΣF = 0 · q·E = q·v·B₁
E = v·B₁ = 10⁶ · 0.02 = 2·10⁴ V/m
v =
E
B₁
v
∥
= v·cosθ · v
⊥
= v·sinθ
F
∥
= q·v
∥
·B₂·sin0° = 0
F
⊥
= q·v
⊥
·B₂ =
m·v
⊥
²
R
d = v
∥
·T · T =
2π·m
q·B₂
B
מדוד
= |B₂|·|cos(α − α₀)|
|B₂| = 50 mT = 0.05 T · α₀ = 50°
140° − 50° = 90° · 50·cos50° = 32.1 mT
6
▾
✕
F = B·I·ℓ | I =
ε
r
| Φ = B·A
ε
ind
=
ΔΦ
Δt
= B·ℓ·v | I
ind
=
B·ℓ·v
R
5.0 V
0.360 kg
1.80 T
7.2 Ω
0.050 kg
2.50
3.60
3.60
0.360
0.00
0.00
0.000
0.00
0.50
1.74
ΣF = 0 , F
mag
= T
F = I·ℓ × B
T = mg
B·I·ℓ = T = mg
I =
ε
r
B·
ε
r
·ℓ = mg
m =
B·ε·ℓ
r·g
T · V · m
Ω · m/s²
= kg
Φ = B·A , A = ℓ·x
ε
ind
=
ΔΦ
Δt
= B·ℓ·
Δx
Δt
= B·ℓ·v
F = q·v × B
mg = B·I·ℓ
I =
ε
ind
R
=
B·ℓ·v
R
mg = B·
B·ℓ·v
R
·ℓ =
B²·ℓ²·v
R
v =
m·g·R
B²·ℓ²
v =
0.05 · 10 · 7.2
1.8² · 0.8²
=
3.6
2.0736
= 1.74 m/s
ε
ind
= 1.8 · 0.8 · 1.74 = 2.5 V
I =
2.5
7.2
= 0.347 A
F = 1.8 · 0.347 · 0.8 = 0.50 N = mg
F = q·v × B
→
🏠
♿