【2027 DSE】物理 電和磁 Electricity and Magnetism 温唔切？公式表＋失分位一文睇清

電流與電荷

★ I_av = Q / t

由某截面在一段時間內通過的電荷，求平均電流；恆定電流時 Q = It。

Find average current from charge passing a cross-section in a given time; for constant current, Q = It.

Q 是電荷量，不是電子數目；電子流向與傳統電流方向相反。

Q is charge, not the number of electrons. Electron flow is opposite to conventional current.

電勢差與電動勢

★ V = E_transferred / Q

★ ε = E_supplied / Q

電勢差是元件每單位電荷轉移的能量；電動勢是電源每單位電荷提供的能量。

Potential difference measures energy transferred per charge in a component; e.m.f. measures energy supplied per charge by a source.

電動勢不是力；有內阻且供電時，端電壓一般小於電動勢。

E.m.f. is not a force. A source delivering current through internal resistance generally has terminal voltage below its e.m.f.

電阻與歐姆定律

★ V = I R

連繫同一元件兩端電壓與通過它的電流；電阻恆定才有 V 與 I 成正比。

Relate voltage across a component to current through it. Proportionality between V and I requires constant resistance.

不能假設燈絲或二極管的電阻恆定；先看圖像是 V–I 還是 I–V。

Do not assume constant resistance for a filament lamp or diode. Check whether the graph is V against I or I against V.

電阻率

R = ρ l / A

求均勻導線的電阻；l 是導線長度，A 是橫截面積。

Find resistance of a uniform wire; l is length and A is cross-sectional area.

金屬線或箔拉長時，長度及橫截面積都可能改變，不能只考慮長度；圓線的 A 應由半徑計算。 [R4]

Stretching a wire or foil can change both length and cross-sectional area; account for both. Calculate a round wire’s A from its radius.

串聯與並聯電阻

R_series = R₁ + R₂ + …

1 / R_parallel = 1 / R₁ + 1 / R₂ + …

串聯元件電流相同；並聯支路兩端接在同一對節點，電壓相同。

Series components share the same current; parallel branches share the same two nodes and voltage.

不能只憑圖上排列判斷串並聯；並聯計算後須取倒數，總電阻小於最小支路電阻。

Judge connections by nodes, not visual layout. Invert the parallel sum; the result is below the smallest branch resistance.

含內阻電源

★ ε = I (R + r)

★ V = ε − I r

電源向外電阻 R 供電，r 為內阻；V 是電源端電壓。

For a source delivering current to external resistance R with internal resistance r, V is terminal voltage.

求電流時勿漏計內阻；第二式的負號適用於電源供電，不能不加判斷套用於充電。

Include internal resistance when finding current. The minus sign is for a source delivering current, not automatically for charging.

電功率、電能與輸電損耗

P = V I = I² R

★ P = V² / R

★ E = P t

各量須屬同一元件；E = Pt 中 P 為恆定或該段時間的平均功率。輸電損耗用線路電流及電阻；交流純電阻平均功率用有效值。

Use quantities for the same component. In E = Pt, P is constant or interval-average power. Cable loss uses cable current and resistance; mean a.c. resistor power uses r.m.s. values.

不能把輸電電壓當成電纜壓降代入 V²/R；kWh 是能量單位，1 kWh = 3.6 × 10⁶ J。

Transmission voltage is not the cable voltage drop for V²/R. The kWh is an energy unit: 1 kWh = 3.6 × 10⁶ J.

庫侖定律

F = |Q₁ Q₂| / (4π ε₀ r²)

求真空中兩個點電荷間的靜電力大小；空氣通常可作近似。方向另按電荷正負判斷。

Find the force magnitude between point charges in vacuum, often approximated by air. Determine direction separately from the signs.

多個電荷的力須作向量相加；r 是電荷間距，不是某個電荷的半徑。

Add forces from multiple charges as vectors. r is charge separation, not the radius of a charge.

電場強度

★ E = F / Q

E = |Q| / (4π ε₀ r²)

E = V / d

依次為電場定義、點電荷場強大小，以及忽略邊緣效應的平行板均勻電場；首式以正試驗電荷判斷方向。

These give the field definition, point-charge field magnitude and uniform parallel-plate field, neglecting edge effects. Use a positive test charge to define direction.

負電荷所受力與電場方向相反；E = V/d 不適用於一般非均勻電場。

Force on a negative charge opposes the field. E = V/d is not a general relation for a non-uniform field.

電流產生的磁場

B = μ₀ I / (2π r)

B = μ₀ N I / l

第一式適用於長直導線，r 為到導線的垂直距離；第二式適用於長空芯螺線管內部，N 是總匝數。

The first is for a long straight wire with perpendicular distance r; the second is inside a long air-core solenoid with N turns.

須先辨認磁場來源，不能因為題目涉及電流就套用長直導線公式；N/l 才是單位長度匝數。 [R5]

Identify the field source first; not every current-related problem uses the straight-wire formula. Turns per unit length are N/l.

載流導線的磁力

F = B I l sin θ

求均勻磁場中直導線所受磁力大小；l 是處於磁場內的長度，θ 是電流與磁場的夾角。

Find the force on a straight wire in a uniform field; l is the length within the field and θ the angle between current and field.

導線平行磁場時磁力為零；計算大小後仍須用方向規則判斷力的方向。

Force is zero for a wire parallel to the field. Determine its direction separately using the appropriate hand rule.

運動電荷的磁力

F = B |Q| v sin θ

★ r = m v / (B |Q|)

第一式求磁力大小；第二式須速度垂直均勻磁場，且磁力提供全部向心力。

The first gives force magnitude. The radius relation requires velocity perpendicular to a uniform field with magnetic force supplying the entire centripetal force.

電荷正負影響偏轉方向；磁力垂直速度，因此單靠磁力不會改變速率。

Charge sign changes the deflection direction. Magnetic force is perpendicular to velocity, so it alone does not change speed.

磁通量

★ Φ = B A cos θ

求均勻磁場穿過平面線圈一匝的磁通量；θ 是磁場與面積法線的夾角。

Find flux through one turn of a planar coil in a uniform field; θ is measured between the field and the area normal.

不要把 θ 當成磁場與線圈平面的夾角；轉動線圈時須考慮投影面積。

Do not measure θ from the plane of the coil. Account for projected area as the coil rotates.

法拉第定律

|ε_av| = N |ΔΦ| / Δt

由磁通量改變求 N 匝線圈的平均感應電動勢大小；Φ 是每匝相同的磁通量，方向另用楞次定律判斷。

Find the magnitude of average induced e.m.f. in N turns sharing flux Φ per turn. Determine the direction separately using Lenz’s law.

用的是磁通量改變，不是磁通量本身；不可重複乘匝數。感應效應反抗的是磁通量的改變。

Use flux change, not flux itself; do not count turns twice. The induced effect opposes the change in magnetic flux.

導體切割磁場

★ |ε| = B l v

直導體、移動速度與均勻磁場三者互相垂直時，求導體兩端感應電動勢大小。

Find motional e.m.f. when the straight conductor, its velocity and the uniform field are mutually perpendicular.

有感應電動勢不一定有電流；電流仍需要閉合電路。

An induced e.m.f. does not guarantee current; a closed conducting path is required.

交流有效值

★ I_rms = I₀ / √2

★ V_rms = V₀ / √2

把正弦交流的峰值換成有效值，常用於純電阻的平均發熱功率。

Convert sinusoidal peak values to r.m.s. values, commonly for mean heating power in a pure resistor.

除以 √2 只適用於正弦波；峰至峰值等於峰值的兩倍，不能直接當峰值。

Division by √2 applies to a sinusoid. Peak-to-peak value is twice the peak value.

變壓器

V_p / V_s = N_p / N_s

★ V_p I_p = V_s I_s

以匝數比求電壓比；第二式是理想變壓器的功率關係，適用於相應的輸入與輸出量。

Use the turns ratio for voltage. The second relation expresses power conservation for an ideal transformer using corresponding input and output quantities.

升壓不會同時增加理想輸出電流；實際變壓器有能量損耗，不可直接假設效率 100%。

Stepping up voltage does not also step up ideal output current. A real transformer has losses, so do not automatically assume 100% efficiency.