Correct Answer

Concept & PrincipleElectricalPower System

Option A

Square of flux

Quick Summary: In an electromagnetic attraction relay, the mechanical force of attraction exerted on the armature is directly proportional to the square of the magnetic flux density across the air gap. This force is developed due to the conversion of magnetic energy into mechanical work as the armature moves to close the relay contacts.

💡 Explanation

In an electromagnetic attraction relay, the mechanical force of attraction exerted on the armature is directly proportional to the square of the magnetic flux density across the air gap. This force is developed due to the conversion of magnetic energy into mechanical work as the armature moves to close the relay contacts.

🔢 Key Formulas

$F = \frac{\Phi^2}{2 \mu_0 A}$ — Force proportional to square of flux

$W_m = \frac{1}{2} S \Phi^2$ — Magnetic energy in terms of reluctance $S$

⚙️ Working Principle

The magnetic energy stored in the air gap is given by $W_m = \frac{\Phi^2 l_g}{2 \mu_0 A}$ . The force $F$ is defined as the negative gradient of this energy with respect to the gap length ( $F = -\frac{dW_m}{dl_g}$ ). Differentiating with respect to the air gap $l_g$ results in $F = \frac{\Phi^2}{2 \mu_0 A}$ , showing that the force is proportional to the square of the flux $\Phi$ and inversely proportional to the area of the pole face $A$ .

📌 Key Points

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The force is unidirectional regardless of the direction of the flux.
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For AC relays, the force oscillates at twice the supply frequency ( $2f$ ).
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Saturation of the magnetic core causes the force to deviate from the square law at high currents.
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The relay operates when the electromagnetic force exceeds the restraining spring force.

✅ Advantages

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Simple construction and robust design.
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Very high speed of operation for instantaneous protection.

❌ Disadvantages / Limitations

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Sensitive to current transients (may cause nuisance tripping).
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Requires high MMF to overcome air gap reluctance.

🛠️ Applications / Uses

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Instantaneous overcurrent relays.
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Differential protection schemes.
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Electromagnetic contactors.

📄 Additional Information

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In AC relays, since $\Phi = \Phi_m \sin(\omega t)$ , the force $F \propto \sin^2(\omega t) = \frac{1-\cos(2\omega t)}{2}$ , leading to a pulsating force.
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Option B (Flux) is incorrect because force follows the squared relationship derived from the energy gradient method.
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Option C (Current) is partially true only if the magnetic circuit is linear, but flux is the fundamental direct parameter.

📊 Diagram / Illustration

✅

A is correct — The electromagnetic force in a relay is proportional to the square of the magnetic flux.

Core Concepts Used

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Electromagnetic Attraction Principle Magnetic Energy Density Relay Operating Characteristics

💡 EXAM TIP

Always remember that for any magnetic actuator, force relates to the square of the flux; this is also the fundamental principle behind why hum occurs in AC chokes due to the $2f$ component.

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