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Difficulty: HardElectromagnetism and Induction

A technician sets up an experiment with two electrically isolated wire coils wrapped around a shared soft-iron core. Coil 1 is connected in series with a 12 V12\text{ V} DC power supply and a mechanical switch. Coil 2 is connected directly to a sensitive center-zero galvanometer. The switch is closed and kept closed until current stabilizes, after which the switch is abruptly opened. What behavior will the galvanometer display during the period of steady current and at the exact instant the switch is opened?

  1. A
    The meter registers a steady, continuous deflection during steady current, then drops smoothly to zero without deflecting when the switch is opened.
  2. The meter reads zero while the current is steady, then momentarily deflects in response to the rapidly collapsing magnetic flux when the switch is opened.Answer
  3. C
    The meter reads a constant voltage proportional to the supply voltage at all times because the iron core directly transfers electrical potential between coils.
  4. D
    The meter reads zero during steady current and remains at zero when the switch opens because the magnetic field stores charge like an electrostatic capacitor.

Answer

The meter reads zero while current is steady, but momentarily deflects when the switch is opened due to the rapid collapse of magnetic flux.
Electromagnetic induction strictly requires a changing magnetic flux cutting through a conductor (Vinduced=−NΔΦΔtV_{\text{induced}} = -N \frac{\Delta \Phi}{\Delta t}). While steady DC current flows in the primary coil, the magnetic field is static, producing no voltage in the secondary coil (meter reads zero). When the switch is opened, the magnetic field collapses rapidly to zero, generating a steep rate of flux change that induces a momentary voltage spike, causing the galvanometer to deflect briefly.

Step-by-Step Solution

1
Analyze the electromagnetic state during steady-state DC current flow.
Magnetic flux is constant (ΔΦΔt=0\frac{\Delta \Phi}{\Delta t} = 0), resulting in 0 V0\text{ V} induced in the secondary coil.
According to Faraday's Law of Electromagnetic Induction (Vinduced=−NΔΦΔtV_{\text{induced}} = -N\frac{\Delta \Phi}{\Delta t}), an electromotive force is generated only when magnetic flux changes over time.
2
Analyze the electromagnetic transition at the instant the primary switch is opened.
Current drops abruptly from steady-state value to zero, causing a rapid collapse of magnetic flux (ΔΦΔt≠0\frac{\Delta \Phi}{\Delta t} \neq 0).
The sudden collapse of magnetic lines of force cuts across the secondary windings, inducing a transient voltage pulse and causing a momentary galvanometer deflection.
3
Synthesize the two operational states to evaluate secondary meter response.
The meter must read zero during steady current and show a sharp, temporary deflection when the circuit is broken.
Combines Faraday's requirement for dynamic flux with the transient behavior of inductive circuits.

Key Concept

Faraday's Law of Electromagnetic Induction and transient flux changes
Estimated Time:1m 30s
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Topics

Electromagnetism and Induction

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