A conductor of length 5 m moves at an angle 30° to the directi... | Technical Ability MCQ | Examoogle

Technical AbilityElectrical Machines and Electromagnetic Induction

A conductor of length 5 m moves at an angle 30° to the direction of the magnetic field of flux density 1.4 wb/m 2 . If the velocity of the conductor is 40 m/s, then calculate the EMF induced in it.

140 volts

100 volts

1400 volts

0 volt

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnical AbilityElectrical Machines and Electromagnetic Induction

Option A

140 volts

Quick Summary:

The induced EMF in a conductor moving through a magnetic field is defined by the motional EMF equation. Given length $l = 5\,\text{m}$ , magnetic flux density $B = 1.4\,\text{Wb/m}^2$ , velocity $v = 40\,\text{m/s}$ , and angle $\theta = 30°$ , the EMF is calculated using $e = \text{Blv} \sin\theta$ .

⚙️TETechnical SolutionConcept & Principle

📜 Standard Reference & Code Clause

Faraday's Law of Electromagnetic Induction (Maxwell's Equations)

💡 Explanation

🔢 Key Formulas

$e = B l v \sin\theta$ — Motional EMF induced in a conductor

⚙️ Working Principle

When a conductor moves through a magnetic field, the Lorentz force acts on the charge carriers within the conductor. This force causes charge separation, resulting in a potential difference (EMF) across the ends of the conductor. The magnitude depends on the orientation of the velocity vector relative to the magnetic field lines, represented by the $\sin\theta$ term.

📌 Key Points

▸
The maximum EMF is induced when the velocity is perpendicular to the magnetic field ( $\theta = 90°$ )
▸
No EMF is induced if the conductor moves parallel to the magnetic field lines ( $\theta = 0°$ )
▸
The SI unit of induced EMF is Volts (V)

✅ Advantages

▸
Direct conversion of mechanical energy to electrical energy
▸
Fundamental principle for all rotating electrical machines like generators

❌ Disadvantages / Limitations

▸
Requires relative motion for constant flux
▸
Prone to eddy current losses if the conductor is solid and not laminated

🛠️ Applications / Uses

▸
DC Generators
▸
Electromagnetic flow meters

📄 Additional Information

▸
Calculation: $e = 1.4 \times 5 \times 40 \times \sin(30°) = 1.4 \times 5 \times 40 \times 0.5 = 140\,\text{V}$ .
▸
Option B (100V) and Option C (1400V) result from incorrect substitution or omission of the $\sin\theta$ component.

📊 Diagram / Illustration

✅

A is correct — The calculated EMF using the formula $e = B l v \sin\theta$ results in exactly $140\,\text{V}$ .

Core Concepts Used

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Faraday's Law Lorentz Force Motional EMF

💡 EXAM TIP

Always verify if the angle provided is between the velocity vector and the magnetic field lines; if given between the conductor length and the field, use $\cos\theta$ instead.

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