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The energy storing capacity of the magnetic field is about ________ times greater than that of the electric field.

A) 50,000

B) 25,000

C) 10,000

D) 40,000

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalMachine

Option B

25,000

Quick Summary:

In electromechanical energy conversion devices (like transformers, motors, and generators), magnetic fields are used as the coupling medium because ferromagnetic materials possess an extremely high energy storage density compared to air or electric field media. For practical operating limits, the magnetic energy density is roughly 25,000 times greater than the electric energy density attainable before dielectric breakdown occurs in air.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$W_m = \frac{1}{2} \frac{B^2}{\mu_0}$ — Magnetic energy density in air/free space (J/m³)

$W_e = \frac{1}{2} \epsilon_0 E^2$ — Electric energy density in air/free space (J/m³)

$\text{Ratio} = \frac{W_m}{W_e} = \frac{B^2}{\mu_0 \epsilon_0 E^2} \approx 25,000$ — Relative energy storage capability ratio

⚙️ Working Principle

The energy stored per unit volume in a magnetic field is given by $W_m = \frac{1}{2} \frac{B^2}{\mu}$ , while for an electric field it is $W_e = \frac{1}{2} \epsilon E^2$ . In practical air-gap applications, taking typical limit values of magnetic flux density ( $B \approx 1.5\text{ T}$ ) and dielectric strength of air ( $E \approx 3 \times 10°6\text{ V/m}$ ), the ratio $\frac{W_m}{W_e}$ evaluates to approximately 25,000.

📌 Key Points

▸
Practical limit for magnetic flux density in air-gap electrical machines is around $B \approx 1.5\text{ T}$ (due to iron saturation).
▸
Practical limit for electric field intensity in air is bounded by dielectric breakdown strength ( $E \approx 3 \times 10°6\text{ V/m}$ ).
▸
Because of this massive factor (~25,000), almost all heavy power electromechanical devices use magnetic fields rather than electric fields as the conversion medium.

✅ Advantages

▸
Allows compact design of electrical machinery operating at high power levels.
▸
Magnetic field coupling provides much higher torque density compared to electrostatic devices.

❌ Disadvantages / Limitations

▸
Magnetic materials suffer from core losses (hysteresis and eddy current losses).
▸
Ferromagnetic saturation limits the maximum feasible magnetic energy density.

🛠️ Applications / Uses

▸
Design of electric motors, generators, transformers, and heavy-duty actuators.
▸
Electromechanical energy conversion systems working on magnetic principles.

📄 Additional Information

▸
Substituting standard constants: $\mu_0 = 4\pi \times 10°{-7}\text{ H/m}$ , $\epsilon_0 = 8.854 \times 10°{-12}\text{ F/m}$ , $B = 1.5\text{ T}$ , and $E = 3 \times 10°6\text{ V/m}$ yields $W_m \approx 8.95 \times 10°5\text{ J/m}^3$ and $W_e \approx 39.8\text{ J/m}^3$ .
▸
Taking the ratio gives $\frac{8.95 \times 10°5}{39.8} \approx 22,500 \approx 25,000$ .
▸
Options A (50,000), C (10,000), and D (40,000) deviate significantly from this standard theoretical and empirical constant used in electrical machine theory.

📊 Diagram / Illustration

✅

B is correct — Substituting typical maximum operating values for magnetic flux density ( $1.5\text{ T}$ ) and electric field breakdown limits ( $3\text{ MV/m}$ ) into their energy density formulas yields a magnetic energy capacity approximately 25,000 times greater than that of the electric field.

Core Concepts Used

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Magnetic Energy Density Electric Energy Density Electromechanical Energy Conversion

💡 EXAM TIP

Always remember that electrostatic devices (capacitive coupling) are restricted to micro-scale or low-power MEMS applications due to air breakdown, while power machinery strictly uses magnetic coupling.

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