Electromagnetism

1. Electrostatics

• Coulomb's Law: the force between two point charges: F = k·q₁·q₂ / r², where k ≈ 9×10⁹ N·m²/C². The force is repulsive if charges have the same sign, attractive if opposite.
• Electric field: E = F/q = k·Q/r² (field created by a point charge Q, at distance r). Field points away from positive charges, toward negative charges.
• Electric potential: V = k·Q/r (a scalar, not a vector — signs of charge matter directly, no separate "direction").

Common mistakes: forgetting Coulomb's law force falls off with r² (not r); confusing electric field (a vector, N/C) with electric potential (a scalar, volts) — they are related but not the same quantity.

2. Direct Current (DC) Circuits

• Ohm's Law: V = IR (voltage = current × resistance).
• Series circuits: same current through every component; total resistance R_total = R₁ + R₂ + ... (resistances simply add).
• Parallel circuits: same voltage across every branch; total resistance follows 1/R_total = 1/R₁ + 1/R₂ + ... (so R_total is always LESS than the smallest individual resistor).
• Power: P = VI = I²R = V²/R (three equivalent forms — pick whichever quantities are known).

Common mistakes: adding resistors in parallel the same way as series (forgetting the reciprocal relationship); using P=V²/R with the wrong voltage when resistors are in series (each resistor has a different voltage drop, not the full source voltage).

3. Magnetic Field

• Magnetic force on a current-carrying wire: F = BIL·sin(θ), where θ is the angle between the wire (current direction) and the magnetic field B.
• Lorentz force (force on a moving charge in a magnetic field): F = qvB·sin(θ), where θ is the angle between velocity v and field B. Direction found via the right-hand rule.

Common mistakes: forgetting the sin(θ) factor — force is maximum when the wire/charge moves perpendicular to B, and zero when parallel to B; mixing up which right-hand-rule convention applies to force vs. field direction.

4. Electromagnetic Induction

• Faraday's Law: induced EMF is proportional to the rate of change of magnetic flux: EMF = −N·(ΔΦ/Δt), where N is the number of coil turns and Φ = B·A·cos(θ) is the magnetic flux.
• Lenz's Law: the induced current always flows in a direction that opposes the change in flux that created it (this is the source of the minus sign in Faraday's law).

Common mistakes: forgetting flux depends on the angle between the field and the area's normal vector (Φ = BA·cos(θ), not just BA); misapplying Lenz's law by predicting the induced current reinforces the change instead of opposing it.