Physics: Electricity and Magnetism

Physics: Electricity and Magnetism

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

• Electric charge is a conserved, quantized property (in coulombs, C) that creates an electric field around itself and experiences a force in the field of another charge.
• Coulomb’s law: F = k q₁q₂ / r², where k ≈ 9 × 10⁹ N·m²/C² and r is the centre-to-centre separation. Like charges repel, unlike charges attract.
• Ohm’s law: V = IR, where V is in volts, I in amperes, R in ohms. Power dissipated: P = VI = I²R = V²/R, in watts.
• Series circuits carry the same current through every component; parallel circuits share the same voltage across each branch.
• Magnetic force on a moving charge: F = qvB sin θ. Faraday’s law: induced EMF ε = −N dΦ/dt, with Lenz’s law giving the current direction.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Electric Charge and Field

Charge is quantized in integer multiples of the elementary charge e = 1.6 × 10⁻¹⁹ C and is conserved in every isolated process. The electric field E at a point is defined as force per unit positive test charge, E = F/q. For a point charge Q, E = kQ/r² points radially outward (positive Q) or inward (negative Q). Electric potential V at a point equals the work done per unit charge in bringing a test charge from infinity; for a point charge V = kQ/r. Potential is a scalar measured in volts (J/C), and potential energy U = qV.

Current Electricity

Current I = Q/t is the rate of charge flow (amperes). Drift velocity v_d = I / (nAe), where n is the free-electron density. Ohm’s law holds only for ohmic conductors at constant temperature: V = IR. Real resistors obey it within a linear range; filament bulbs and diodes are non-ohmic.

Series vs Parallel Rules

Quantity	Series	Parallel
Current	Same through all	Splits across branches
Voltage	Splits across components	Same across each branch
Resistance	R_total = Σ Rᵢ	1/R_total = Σ 1/Rᵢ
Capacitance	1/C_total = Σ 1/Cᵢ	C_total = Σ Cᵢ

Magnetism and Induction

A current-carrying conductor produces a magnetic field encircling it; the right-hand grip rule gives the direction. A straight wire of length L in field B carrying current I experiences F = BIL sin θ. Faraday’s law states that a changing magnetic flux Φ = BA cos θ through a coil of N turns induces ε = −N dΦ/dt. Lenz’s law (the negative sign) says the induced current opposes the change that produces it.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases and Quantitative Traps

• Unit conversions trip most NAT-I candidates: 1 kV = 1000 V, 1 mA = 10⁻³ A, 1 µF = 10⁻⁶ F. A 6 kΩ resistor across 12 V carries I = V/R = 0.002 A = 2 mA, not 2 A.
• Power in mixed circuits: total power equals the sum of branch powers, P_total = Σ VᵢIᵢ. In parallel, each branch sees the full source voltage, so a lower-resistance branch dissipates more power.
• AC versus DC: AC quantities are usually quoted as RMS values (V_rms = V_peak / √2, I_rms = I_peak / √2). The average power in AC is P = V_rms · I_rms · cos φ, where φ is the phase angle between V and I; for a pure resistor φ = 0 and cos φ = 1.
• Capacitor energy: a capacitor stores U = ½CV² = Q²/(2C) = ½QV. A capacitor blocks DC at steady state (no current through the dielectric) but passes AC, with reactance X_C = 1/(2πfC).

Connections and Common Mistakes

• Right-hand rule confusion: for the field around a wire, thumb with current, fingers curl with B; for the force on a wire, fingers point along I and curl to B, thumb gives F.
• Faraday sign: include the negative sign only when the question asks for current direction; for magnitude, use |ε| = N|ΔΦ/Δt|.
• Worked micro-example: a coil of 200 turns has its flux change from 0.5 Wb to 0.1 Wb in 0.02 s. ε = −200 × (0.1 − 0.5)/0.02 = 4000 V, and by Lenz’s law the induced current opposes the flux drop.
• Exam strategy: NAT-I tests Ohm’s law and series-parallel combinations in roughly 4% of the Subject Knowledge paper — focus on numeric drills with mixed units rather than derivations.

Practice Prompts

1. Two 6 Ω resistors in parallel are connected in series with a 4 Ω resistor across a 16 V battery. Find the current through the 4 Ω resistor and the voltage across the parallel combination.
2. A 50-turn coil of area 0.02 m² is withdrawn from a uniform 0.4 T field in 0.1 s. Calculate the magnitude of the induced EMF and justify the direction of the induced current.

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