IP Physics Notes (Upper Secondary, Year 3-4): 16) Electromagnetic Induction

Quick recap -- Changing magnetic flux induces emf. Remember: faster change -> larger emf, and the induced current always opposes the flux change (Lenz). Generators and transformers are direct applications.

Faraday's & Lenz's Laws

• Faraday: magnitude of induced emf \( \mathcal{E} \) is proportional to rate of change of magnetic flux linkage.
• Lenz: induced current direction opposes the change producing it (conservation of energy).
• Practical consequences:
  • Move magnet faster -> larger \( \mathcal{E} \).
  • Use stronger magnet or more coil turns -> larger \( \mathcal{E} \).
  • No change in flux -> no induction.

Induction Setups

• Pushing/pulling magnet through coil.
• Moving a conductor across magnetic field lines.
• Rotating a coil in a uniform magnetic field (basis of AC generator).
• Use right-hand grip rule to infer the induced polarity that opposes the motion (e.g., approaching north pole induces north on near face of coil).

Alternating-Current Generator

• Coil rotates in magnetic field; flux linkage varies sinusoidally.
• Slip rings maintain continuous connection; output is AC.
• Peak emf depends on rotation speed, flux density, and coil turns.
• Voltage-time graph: sine wave crossing zero twice per revolution; faster rotation increases frequency.

Transformers

• Two coils wound on common soft-iron core; only works with AC (changing flux required).
• Ideal transformer equations: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s}, \quad V_p I_p = V_s I_s \]
  • Step-up: \( N_s > N_p \) -> voltage increases, current decreases.
  • Step-down: \( N_s < N_p \) -> voltage decreases, current increases.
• Real transformers suffer losses:
  • Copper loss: \( I^2 R \) heating; mitigated with low-resistance windings.
  • Eddy currents: reduced via laminated cores.
  • Hysteresis: reduced by soft iron core.
  • Flux leakage: minimised by tight coupling between coils.

Worked Example: Step-Down Calculation

The primary voltage is \[ \pu{11 kV}, N_p = 3,300, N_s = 110 \]

The secondary voltage is \[ V_s = V_p (N_s/N_p) = 11,000 \times 110 / 3,300 \approx 3.67 \times 10^2 \space \pu{V} \]

Assuming ideal behaviour, \[ I_s = P / V_s \approx 2.73 \times 10^2 \pu{A} \]

so the primary current is \[ I_p = I_s V_s / V_p \approx 9.2 \space \pu{A} \]

Power Transmission Rationale

• Power delivered: \( P = V I \).
• Transmission loss in cables: \( P_\text{loss} = I^2 R_\text{cable} \).
• Step-up to high voltage -> smaller current -> dramatically lower \( I^2 R \) losses.
• Step-down near consumers for safe household voltages.

Key Takeaways

• Identify flux changes: moving magnet/coil, changing area, changing field strength.
• Lenz's law gives induced current direction; the induced field always resists the cause.
• Transformers rely on AC; memorise ratio equations and common loss-reduction techniques.
• In transmission questions, emphasise "high voltage -> low current -> reduced \( I^2 R \) losses" to justify design choices.