Chapter 11: Formula Reference — Electricity and Magnetism
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11.1 Electrostatics
Quantity / Law | Formula | Symbols & SI Units |
|---|---|---|
Coulomb's Law | F = kq₁q₂/r² | k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C², q₁, q₂ = charges (C), r = separation (m) |
Electric field | E = F/q = kQ/r² | E in N/C or V/m |
Electric potential | V = W/q = kQ/r | V in volt (V) |
Electric potential energy | U = kq₁q₂/r | U in joule (J) |
Capacitance | C = Q/V | C in farad (F), Q = charge (C), V = potential difference (V) |
Parallel plate capacitor | C = ε₀A/d | A = plate area (m²), d = separation between plates (m) |
Current electricity deals with the flow of electric charge through a conductor, driven by a potential difference. Ohm's law, discovered by Georg Simon Ohm and one of the most heavily tested relations in this entire syllabus, states that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions (particularly temperature) remain constant.
11.2 Current Electricity
Quantity / Law | Formula | Symbols & SI Units |
|---|---|---|
Electric current | I = Q/t | I in ampere (A), Q = charge (C), t = time (s) |
Ohm's Law | V = IR | V = potential difference (V), I = current (A), R = resistance (Ω) |
Resistance (in terms of resistivity) | R = ρL/A | ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²) |
Resistors in series | R = R₁ + R₂ + R₃ + ... | Equivalent resistance is the sum |
Resistors in parallel | 1/R = 1/R₁ + 1/R₂ + 1/R₃ + ... | Reciprocal of equivalent resistance is the sum of reciprocals |
Electric power | P = VI = I²R = V²/R | P in watt (W) |
Electrical energy consumed | E = Pt | E in joule (J), or in kWh for commercial billing (1 unit = 1 kWh) |
Heating effect of current (Joule's Law) | H = I²Rt | H = heat produced (J) |
Kirchhoff's Current Law (KCL) | Sum of currents entering a junction = sum leaving it | Based on conservation of charge |
Kirchhoff's Voltage Law (KVL) | Sum of potential differences around a closed loop = 0 | Based on conservation of energy |
11.3 Magnetism
Quantity / Law | Formula | Symbols & SI Units |
|---|---|---|
Force on a moving charge (magnetic) | F = qvB sinθ | q = charge (C), v = velocity (m/s), B = magnetic flux density (T), θ = angle between v and B |
Force on a current-carrying conductor | F = BIL sinθ | I = current (A), L = length of conductor in field (m) |
Magnetic flux | Φ = BA cosθ | Φ in weber (Wb), A = area (m²) |
Faraday's Law of Electromagnetic Induction | EMF = −dΦ/dt | EMF induced is proportional to the rate of change of magnetic flux |
Lenz's Law | Induced EMF opposes the change in flux that produces it | Consequence of conservation of energy |
Self-inductance | EMF = −L(dI/dt) | L = self-inductance (henry, H) |
Magnetic field due to a long straight current-carrying wire | B = μ₀I/2πr | μ₀ = permeability of free space = 4π × 10⁻⁷ T·m/A, r = distance from wire (m) |