The magnetic force on a current-carrying conductor is maximum ... | General Science MCQ | Examoogle

General SciencePhysics: Electromagnetism

The magnetic force on a current-carrying conductor is maximum when the angle between the conductor and the magnetic field is:

0 degrees

45 degrees

90 degrees

180 degrees

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Electromagnetism

Option C

90 degrees

Quick Summary:

The magnetic force on a current-carrying conductor is determined by the cross product of the current vector and the magnetic field vector. The magnitude of this force is proportional to the sine of the angle between the conductor and the magnetic field; therefore, it is maximum when $\sin(\theta) = 1$ , which occurs at $90°$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of catching the wind with a sail; the sail catches the maximum force of the wind when it is held perpendicular to the wind's direction rather than parallel to it.

🧠 Memory Mnemonic / Shortcut Aid

Sine is 'Strongest' at 'Seventy-plus-twenty' (i.e., $90°$ ).

🔢 Key Formulas

$F = I L B \sin(\theta)$ — The magnetic force formula where $\theta$ is the angle between the conductor and magnetic field.

⚙️ Working Principle

The force $F$ experienced by a conductor of length $L$ carrying current $I$ in a uniform magnetic field $B$ is given by $F = I L B \sin(\theta)$ . Since the sine function reaches its maximum value of $1$ at an angle of $90°$ , the force becomes maximum ( $F = ILB$ ) when the conductor is placed perpendicular to the field lines.

📌 Key Points

▸
At $0°$ and $180°$ , $\sin(\theta) = 0$ , meaning the conductor experiences zero magnetic force.
▸
The direction of the force is determined by Fleming's Left-Hand Rule.
▸
Magnetic force is a vector quantity dependent on the orientation of the wire.

🛠️ Applications / Uses

▸
Electric motors work on this principle by optimizing the angle of current-carrying coils in magnetic fields.
▸
Galvanometers use this force to measure electric current.

📄 Additional Information

▸
Standard unit for magnetic force is the Newton (N).
▸
Option A ( $0°$ ) and Option D ( $180°$ ) result in zero force because the conductor is parallel to the field lines.
▸
Option B ( $45°$ ) results in a force of $F = \frac{ILB}{\sqrt{2}}$ , which is less than the maximum value.

📊 Diagram / Illustration

✅

C is correct — The magnetic force is maximum when the conductor is perpendicular to the magnetic field, as $\sin(90°) = 1$ .

Core Concepts Used

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Lorentz Force Electromagnetism Trigonometric variation of sine function

💡 EXAM TIP

Always remember that for dot products (like Magnetic Flux $\Phi = B A \cos(\theta)$ ), the maximum occurs at $0°$ , while for cross products (like Force $F = q v B \sin(\theta)$ ), the maximum occurs at $90°$ .

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