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General SciencePhysics: Electromagnetism

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If a uniform magnetic field is parallel to the plane of a surface, the magnetic flux through the surface is _______.

infinite

zero

maximum

half of maximum

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Electromagnetism

Option C

maximum

Quick Summary:

The magnetic flux through a surface is defined as the number of magnetic field lines passing perpendicular to the area. If the magnetic field is parallel to the plane of the surface, the angle between the magnetic field vector and the area vector is $90°$ , resulting in zero magnetic flux.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Imagine holding a flat sheet of paper parallel to a steady stream of water (the magnetic field); none of the water passes through the surface of the paper.

🧠 Memory Mnemonic / Shortcut Aid

Flux is flow: If the flow is parallel to the 'wall', it hits nothing—so Flux is zero.

🔢 Key Formulas

$\Phi_B = \vec{B} \cdot \vec{A}$ — Definition of magnetic flux as a dot product

$\Phi_B = BA \cos(\theta)$ — Scalar form involving the angle with the normal

⚙️ Working Principle

The magnetic flux $\Phi_B$ is calculated using the dot product $\Phi_B = \vec{B} \cdot \vec{A} = BA \cos(\theta)$ , where $\theta$ is the angle between the magnetic field $\vec{B}$ and the normal vector $\vec{A}$ to the surface. When the field is parallel to the plane, it is perpendicular to the normal vector, meaning $\theta = 90°$ . Since $\cos(90°) = 0$ , the magnetic flux is zero.

📌 Key Points

▸
Magnetic flux is a scalar quantity.
▸
The area vector $\vec{A}$ is always defined as normal (perpendicular) to the surface.
▸
Maximum flux occurs when the field lines are perpendicular to the surface ( $\theta = 0°$ ).

🛠️ Applications / Uses

▸
Design of electric generators
▸
Understanding electromagnetic induction

📄 Additional Information

▸
The SI unit of magnetic flux is the Weber ( $Wb$ ).
▸
Option C is incorrect as labeled in the prompt; the correct answer is Option B because when $\theta = 90°$ , $\cos(90°) = 0$ .

📊 Diagram / Illustration

✅

B is correct — If the magnetic field is parallel to the surface, the angle between the field and the area normal is $90°$ , making the dot product $\cos(90°)$ equal to zero.

Core Concepts Used

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Magnetic Flux Dot Product Area Vector

💡 EXAM TIP

Always identify the direction of the area vector (the normal) first in flux problems to avoid common sign or ratio errors.

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