Electromagnetism and circuits

Electromagnetism describes the interaction between electric currents and magnetic fields. When current flows through a conductor, it generates a magnetic field in concentric circles around the wire (right-hand grip rule: thumb shows current direction, fingers curl in field direction).

Key Terms:

• Magnetic flux density (B): strength of magnetic field, measured in tesla (T)
• Electromagnetic induction: generation of electromotive force (emf) when magnetic flux through a conductor changes
• Faraday's Law: induced emf is proportional to rate of change of magnetic flux linkage
• Lenz's Law: induced current opposes the change causing it

Essential Equations:

• Force on current-carrying conductor: F = BIL sin θ (F in N, B in T, I in A, L in m)
• Induced emf: ε = -N(ΔΦ/Δt) where Φ = BA (flux linkage)
• Magnetic flux: Φ = BA cos θ (Wb or T·m²)

Circuits Fundamentals:

• Ohm's Law: V = IR (voltage, current, resistance relationship)
• Kirchhoff's Current Law (KCL): sum of currents entering junction equals sum leaving
• Kirchhoff's Voltage Law (KVL): sum of emfs equals sum of potential differences in closed loop
• Series circuits: same current throughout, voltages add (R_total = R₁ + R₂ + ...)
• Parallel circuits: same voltage across branches, currents add (1/R_total = 1/R₁ + 1/R₂ + ...)
• Power: P = IV = I²R = V²/R (measured in watts)

Mnemonic: "Fleming's Left-hand rule" for motor effect: First finger = Field, seCond = Current, thuMb = Motion.

Electric Motors convert electrical energy to kinetic energy using the motor effect. In a loudspeaker, alternating current in a coil creates varying forces in a magnetic field, making the cone vibrate and produce sound waves. The faster the current changes, the higher the frequency (pitch) produced.

Generators work oppositely: rotating a coil in a magnetic field induces emf through electromagnetic induction. Bicycle dynamos demonstrate this—faster wheel rotation means greater rate of flux change, producing brighter lights. Power stations use massive rotating coils (turbines) turned by steam, water, or wind.

Analogy for Circuits: Think of electric circuits like water flowing through pipes:

• Voltage = water pressure (drives flow)
• Current = flow rate (litres per second)
• Resistance = pipe narrowness (opposes flow)
• Battery = pump (maintains pressure difference)

In series circuits, water flows through one narrow pipe then another—flow rate stays constant but pressure drops across each restriction. In parallel circuits, water divides between multiple pipes—pressure across each branch is identical but total flow increases.

Transformers in phone chargers use electromagnetic induction between two coils. AC in the primary coil creates changing magnetic flux, inducing voltage in the secondary coil. The voltage ratio equals the turns ratio: V_s/V_p = N_s/N_p. Step-down transformers (N_s < N_p) reduce mains 230V to safe 5V for devices.

Circuit Breakers protect homes using electromagnets. Excess current strengthens the magnetic field until it pulls a switch open, breaking the circuit before wires overheat and cause fires.

Example 1: A wire of length 0.15 m carries a current of 3.0 A perpendicular to a magnetic field of flux density 0.40 T. Calculate the force on the wire.

Solution:

1. Identify given values: L = 0.15 m, I = 3.0 A, B = 0.40 T, θ = 90° (perpendicular)
2. Select formula: F = BIL sin θ
3. Substitute: F = 0.40 × 3.0 × 0.15 × sin 90°
4. Calculate: F = 0.40 × 3.0 × 0.15 × 1 = 0.18 N

Examiner note: Always state direction using Fleming's left-hand rule for full marks.

Example 2: A coil of 200 turns with area 0.025 m² is in a magnetic field of 0.30 T. The field reduces to zero in 0.050 s. Calculate the induced emf.

Solution:

1. Initial flux: Φ₁ = BA = 0.30 × 0.025 = 7.5 × 10⁻³ Wb
2. Final flux: Φ₂ = 0 Wb (field becomes zero)
3. Change in flux: ΔΦ = 7.5 × 10⁻³ Wb
4. Apply Faraday's law: ε = N(ΔΦ/Δt)
5. Substitute: ε = 200 × (7.5 × 10⁻³/0.050)
6. Calculate: ε = 200 × 0.15 = 30 V

Example 3: Three resistors (4Ω, 6Ω, 12Ω) are connected in parallel to a 12V supply. Find total current.

Solution:

1. Find equivalent resistance: 1/R = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12
2. Therefore: R = 2Ω
3. Apply Ohm's law: I = V/R = 12/2 = 6 A

Examiner note: Show working for parallel resistance calculation—common mark allocation point.