A metal rod of length 1.5 m moves with a velocity of 10 m/s th... | Technical MCQ | Examoogle

TechnicalElectrical Engineering

A metal rod of length 1.5 m moves with a velocity of 10 m/s through a uniform magnetic field of 2 T. What is the magnitude of the induced EMF if the rod moves at an angle of 60° to the magnetic field?

30 volts

36 volts

18 volts

26 volts

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnicalElectrical Engineering

Option D

26 volts

Quick Summary:

The motional electromotive force (EMF) induced in a conductor moving through a magnetic field is determined by the formula $\varepsilon = B l v \sin(\theta)$ . Substituting $B = 2\text{ T}$ , $l = 1.5\text{ m}$ , $v = 10\text{ m/s}$ , and $\theta = 60°$ yields $\varepsilon = 2 \times 1.5 \times 10 \times \sin(60°) = 30 \times \frac{\sqrt{3}}{2} \approx 25.98\text{ V}$ , which rounds to 26 V.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a window screen passing through a gust of wind; the 'wind' (magnetic field) only pushes on the screen effectively when the screen is oriented to catch the flow, similar to how the rod must 'cut' the magnetic lines to generate EMF.

🧠 Memory Mnemonic / Shortcut Aid

BLV sin(theta): B-L-V (Believable) Sine-theta.

🔢 Key Formulas

$\varepsilon = B l v \sin(\theta)$ — Motional EMF equation where $\theta$ is the angle between velocity and magnetic field vectors.

$\vec{F}_m = q(\vec{v} \times \vec{B})$ — Lorentz force exerted on charges within the conductor.

⚙️ Working Principle

When a metallic rod moves through a magnetic field, the free electrons in the rod experience a Lorentz force $\vec{F} = q(\vec{v} \times \vec{B})$ . This force causes a redistribution of charge, creating a potential difference across the ends of the rod. The magnitude is proportional to the component of the velocity perpendicular to the magnetic field.

📌 Key Points

▸
Induced EMF is maximum when the conductor moves perpendicular to the magnetic field ( $90°$ ).
▸
Induced EMF is zero when the conductor moves parallel to the magnetic field ( $0°$ ).
▸
The SI unit of induced EMF is the Volt (V).

✅ Advantages

▸
Fundamental principle behind electric generators and dynamos.

❌ Disadvantages / Limitations

▸
Induced currents may cause eddy current heating in stationary conducting parts of machinery.

🛠️ Applications / Uses

▸
AC Generators (Alternators)
▸
Induction heating systems

📄 Additional Information

▸
$\sin(60°) = \frac{\sqrt{3}}{2} \approx 0.866$ .
▸
Calculation: $2 \times 1.5 \times 10 \times 0.866 = 25.98\text{ V}$ .

📊 Diagram / Illustration

✅

D is correct — The induced EMF is calculated as $2 \times 1.5 \times 10 \times \sin(60°) \approx 26\text{ V}$ .

Core Concepts Used

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Motional EMF Lorentz Force Electromagnetic Induction

💡 EXAM TIP

Always verify if the angle $\theta$ is given with the magnetic field vector or the normal to the area; here, it is directly with the field, so use $\sin(\theta)$ .

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