Physics: Electricity and Magnetism

Physics: Electricity and Magnetism

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Electricity and Magnetism unifies two phenomena once thought separate: stationary charges (electrostatics) and moving charges (current) interacting with magnetic fields. The governing relation between charges is Coulomb’s law, F = k q₁q₂ / r², where k ≈ 9 × 10⁹ N·m²/C². A charge q in a field E experiences force F = qE, and the potential difference V = W/q links energy to charge. In circuits, Ohm’s law V = IR and power P = VI = I²R govern resistive networks solved with Kirchhoff’s junction and loop rules. Magnetism enters via the force on a conductor F = BIL sinθ and the induced EMF, EMF = −N dΦ/dt, whose negative sign encodes Lenz’s law. For HAT-UG Subject Knowledge, expect 4–6 MCQs on circuit analysis, Coulomb’s law, and induction.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Electrostatics

Coulomb’s law gives the vector force between point charges: F = k q₁q₂ / r² r̂. The superposition principle lets you sum forces from multiple charges linearly. Every charge creates an electric field E = F/q, and the work done moving a test charge between two points defines potential difference V = W/q, measured in volts (J/C). In a uniform field between parallel plates, E = V/d, and the energy stored is U = ½CV².

Current Electricity

Steady current I = Q/t flows when a potential difference drives charges through a conductor of resistance R = ρL/A, where ρ is resistivity. Ohm’s law V = IR holds only for ohmic conductors. Power dissipated is P = VI = I²R = V²/R. Kirchhoff’s junction rule (ΣI = 0) and loop rule (ΣV = 0) let you solve multi-loop networks.

Combinations Table

Combination	Resistors (R)	Capacitors (C)
Series	R_s = ΣRᵢ	1/C_s = Σ(1/Cᵢ)
Parallel	1/R_p = Σ(1/Rᵢ)	C_p = ΣCᵢ

A classic trap: the formulas invert between R and C — students mix this up routinely.

Magnetism & Induction

A current-carrying wire produces a magnetic field (right-hand grip rule); the Biot-Savart law gives dB = (μ₀/4π) I dl × r̂/r². The force on a current in an external field is F = IL × B, magnitude BIL sinθ. Faraday’s law states EMF = −N dΦ/dt; Lenz’s law fixes the sign so that induced current opposes flux change. A transformer uses mutual induction: Vₛ/Vₚ = Nₛ/Nₚ.

HAT-UG Pattern

Questions blend numericals (find equivalent resistance, time of flight of charge in crossed fields) with conceptual items on Lenz’s sign, RMS vs peak (V_rms = V₀/√2), and conventional current direction.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases & Deeper Mechanisms

The Coulomb force and the magnetic force are manifestations of a single electromagnetic interaction — stationary charges see only the electric field, while moving charges also see a magnetic field that depends on the observer’s frame. This is why relativity unifies them. The magnetic force does no work (it is always perpendicular to velocity); energy transfer in motors happens via the changing flux in the armature coil.

Faraday’s law requires dΦ/dt ≠ 0 — a static field, however strong, produces zero EMF. A conductor moving in a uniform field generates motional EMF ε = BLv sinθ, which is the DC generator principle. In an AC circuit with pure inductance, voltage leads current by 90°; with pure capacitance, current leads voltage by 90°. Real devices (motors, transformers) have non-ideal behaviour: hysteresis losses, eddy currents (reduced by lamination), and copper losses (I²R).

Common Mistakes to Avoid

• Treating potential (V, scalar, J/C) and potential energy (U = qV, scalar, J) as interchangeable.
• Using peak values (V₀, I₀) where the formula requires RMS values for average power: ⟨P⟩ = V_rms I_rms cosφ.
• Applying Fleming’s left-hand rule for motors and right-hand rule for generators — they are mirror images, easy to swap under pressure.
• Ignoring internal resistance r: terminal voltage V_term = EMF − Ir, so the battery is not an ideal source.
• Sign errors in Lenz’s law: induced current opposes the change, not the field itself.

Worked Micro-Example

A 10 Ω resistor and a 20 Ω resistor are in parallel, connected to a 12 V battery of internal resistance 1 Ω. Equivalent external resistance R_p = (10 × 20)/(10 + 20) = 6.67 Ω. Total circuit resistance = 7.67 Ω, so current from battery I = 12/7.67 ≈ 1.56 A. Terminal voltage = 12 − (1.56)(1) = 10.44 V. Power dissipated externally = I²R_p ≈ 16.3 W.

Practice Prompts

1. A coil of 200 turns and area 0.02 m² is perpendicular to a uniform magnetic field changing at 0.5 T/s. Find the magnitude and direction of the induced EMF.
2. Three capacitors 2 μF, 4 μF, and 6 μF are connected (a) all in series, (b) all in parallel. Which arrangement stores more energy at 50 V?

Adjacent Topics

Link this chapter to Modern Physics (electromagnetic waves, photoelectric effect context) and Semiconductors (p-n junction, diode I-V characteristics).

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