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Zorluk: Çok zorFundamentals of Electromagnetism and Induction

A technician wraps two separate copper wire coils, Coil 1 and Coil 2, around a single soft iron core. Coil 1 is connected to a steady 12V DC power supply, and the current has reached a steady state. Coil 2 is connected only to a sensitive digital voltmeter. If the technician rapidly pulls the soft iron core completely out of the coils while Coil 1 remains connected to the power supply, which of the following best describes the reading on the voltmeter during the exact moment the core is moving?

  1. A voltage reading that spikes momentarily and then returns to zero, because the sudden decrease in magnetic permeability causes a rapid change in magnetic flux.Cevap
  2. B
    A continuous reading of zero volts, because a direct current (DC) power supply cannot produce the alternating magnetic field required for electromagnetic induction.
  3. C
    A steady 12V reading, because removing the iron core eliminates the magnetic resistance between the coils, allowing the full electromotive force to transfer.
  4. D
    A permanently higher voltage reading, because the opposing magnetic poles of the iron core are no longer present to attract and restrict the electron flow.

Cevap

The correct answer is a voltage reading that spikes momentarily and then returns to zero, because the sudden decrease in magnetic permeability causes a rapid change in magnetic flux.
Electromagnetic induction requires a changing magnetic flux over time. While a steady DC current normally produces a constant, unchanging magnetic field, the physical act of rapidly removing the highly permeable iron core drastically reduces the magnetic flux. This rapid change in flux induces a temporary voltage spike in the secondary coil. The induction ceases as soon as the core is completely removed, because the flux becomes constant again, returning the voltmeter reading to zero.

Adım Adım Çözüm

1
Analyze the initial steady state of the circuit.
Coil 1 produces a constant magnetic flux that is concentrated by the soft iron core. Because the flux is not changing over time, the induced voltage in Coil 2 is zero.
Faraday's Law of Induction requires a changing magnetic field to induce an electromotive force (EMF).
2
Evaluate the physical change caused by the technician's action.
The technician removes the soft iron core, replacing a material with high magnetic permeability with air, which has very low magnetic permeability.
Magnetic permeability directly determines how well a material can support the formation of a magnetic field within itself.
3
Determine the effect of this physical change on the magnetic flux.
The total magnetic flux passing through both coils drops rapidly as the highly permeable core is removed.
Less permeability means weaker magnetic field strength for the same amount of current.
4
Apply Faraday's Law to the changing magnetic flux.
The rapidly decreasing magnetic flux induces a temporary voltage (a spike) in Coil 2.
An EMF is induced in a coil whenever there is a change in magnetic flux passing through it, proportional to the rate of change (E=−N×ΔΦΔtE = -N \times \frac{\Delta\Phi}{\Delta t}).
5
Determine the final state after the core is completely removed.
The magnetic flux stabilizes at a new, much lower constant value. Since the flux is no longer changing, the induced voltage in Coil 2 returns to zero.
Induction only occurs during the period of change.

Anahtar Kavram

Faraday's Law of Induction and Magnetic Permeability
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Konular

Fundamentals of Electromagnetism and Induction

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