Magnetic flux is defined by the formula:

Question

Examoogle · Accepted Answer

The correct answer is Option B: $\Phi = B A \cos(	heta)$. Magnetic flux ($\Phi$) is the total magnetic field passing through a given surface area. It is defined as the scalar product of the magnetic field vector ($\vec{B}$) and the area vector ($\vec{A}$), resulting in the formula $\Phi = B A \cos(	heta)$, where $	heta$ is the angle between the magnetic field and the normal to the surface.

Step-by-Step Solution & Concepts:
Magnetic flux ($\Phi$) is the total magnetic field passing through a given surface area. It is defined as the scalar product of the magnetic field vector ($\vec{B}$) and the area vector ($\vec{A}$), resulting in the formula $\Phi = B A \cos(	heta)$, where $	heta$ is the angle between the magnetic field and the normal to the surface.

Working Principle: The principle relies on the definition of a scalar product (dot product) of two vectors. Since flux is the measure of the 'flow' of a field through a surface, we only consider the component of the magnetic field perpendicular to the surface area (i.e., $B \cos(	heta)$). When the field is perpendicular to the area, $	heta = 0^\circ$ and $\cos(0) = 1$, yielding maximum flux.

Key Formulas: $\Phi = \vec{B} \cdot \vec{A}$ — Vector dot product representation; $\Phi = B A \cos(	heta)$ — Scalar calculation representation; $	ext{Unit}: 1 	ext{ Weber} (Wb) = 1 	ext{ Tesla} \cdot 	ext{m}^2$

Key Points: Magnetic flux is a scalar quantity.; The area vector $\vec{A}$ is always directed perpendicular to the surface.; Maximum flux occurs when the field lines are perpendicular to the surface ($	heta = 0^\circ$).; Zero flux occurs when the field lines are parallel to the surface ($	heta = 90^\circ$).

Advantages: Helps in calculating electromagnetic induction according to Faraday's Law.

Disadvantages: Requires precise determination of the normal vector to the surface for complex geometries.

Applications: Design of electric generators and transformers.; Understanding the working principle of electric motors.

Additional Info: The SI unit of magnetic flux is the Weber (Wb).. Option A ($\Phi = B A \sin(	heta)$) is incorrect as it would imply zero flux when lines are perpendicular to the surface.. Option C and D are dimensionally incorrect, as flux must have units of Magnetic Field $	imes$ Area.

Answer: B is correct — Magnetic flux is defined by the dot product of the magnetic field and the area vector, which simplifies to $\Phi = B A \cos(	heta)$.

Exam Tip: Always check whether the angle given in the question is with the surface or the normal to the surface. If the angle is with the surface, use $\sin(	heta)$; if it is with the normal, use $\cos(	heta)$.

Examoogle · Answer

Option A: $\Phi = B A \sin(	heta)$

Examoogle · Answer

Option C: $\Phi = \frac{B}{A}$

Examoogle · Answer

Option D: $\Phi = \frac{A}{B}$

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