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For a toroid to extract the energy from the supply system, the flux linkages of the magnetic field must be ________

A) zero

B) changing or varying

C) constant

D) any of the mentioned

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalMachine

Option B

changing or varying

Quick Summary:

According to Faraday's Law of Electromagnetic Induction, an electromotive force (e.m.f.) is induced in a circuit only when there is a change in the magnetic flux linkage over time. For a toroid or any inductive system to continuously exchange or extract energy from an electrical supply, the flux linkages must be changing or varying ( $d\lambda/dt \neq 0$ ).

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$e = -\frac{d\lambda}{dt} = -N \frac{d\Phi}{dt}$ — Faraday's law of electromagnetic induction for induced e.m.f.

$W_f = \int i \, d\lambda$ — Magnetic field energy stored/extracted in terms of flux linkages

$p(t) = e(t) \cdot i(t) = i(t) \frac{d\lambda}{dt}$ — Instantaneous electrical power absorbed by the magnetic field

⚙️ Working Principle

When an alternating or time-varying current flows through the toroidal winding, it produces a time-varying magnetic flux $\Phi(t)$ inside the core. By Faraday's Law, the induced voltage is $e = -\frac{d\lambda}{dt} = -N \frac{d\Phi}{dt}$ . Electrical power transfer $p(t) = e(t) \cdot i(t)$ occurs continuously only when the flux linkage changes, allowing magnetic energy to be absorbed from or returned to the supply system.

📌 Key Points

▸
A constant magnetic flux ( $\,d\lambda/dt = 0\,$ ) yields zero induced voltage, so no continuous power/energy can be extracted from the supply.
▸
Time-varying flux linkage allows continuous energy exchange between the electrical supply and the magnetic field of the toroid.
▸
For static magnetic fields, energy is stored during initial energization, but zero net continuous energy transfer occurs once steady state is reached.

✅ Advantages

▸
Efficient electromechanical energy transfer in AC excitation.
▸
Toroidal shape provides high magnetic efficiency with minimal flux leakage.

❌ Disadvantages / Limitations

▸
Cannot continuously absorb or convert power from a pure DC steady-state source.
▸
Hysteresis and eddy current losses occur due to changing flux linkage.

🛠️ Applications / Uses

▸
Toroidal Transformers and Inductors
▸
Electromechanical Actuators and Energy Converters

📄 Additional Information

▸
Option A (zero) is incorrect because zero flux linkage implies no magnetic field and no stored or transferred energy.
▸
Option C (constant) is incorrect because constant flux linkage results in zero induced e.m.f. ( $e = d\lambda/dt = 0$ ), so no continuous power is drawn from the supply.
▸
Option D is incorrect because only a varying flux linkage satisfies Faraday's law for continuous energy extraction.

📊 Diagram / Illustration

✅

B is correct — Continuous energy extraction from an electrical supply requires a time-varying flux linkage to induce an electromotive force ( $e = d\lambda/dt \neq 0$ ).

Core Concepts Used

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Faraday's Law of Electromagnetic Induction Flux Linkage (\lambda) Electromechanical Energy Conversion

💡 EXAM TIP

Always remember that in static or dynamic magnetic circuits, power transfer requires $e \neq 0$ , which inherently demands time-varying flux linkage ( $d\lambda/dt$ ).

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