Question

What is the SI unit of magnetic flux, is it a vector or scalar quantity?

Answer 1

Hint: Magnetic flux is defined by the number of magnetic lines passing through a specific closed area. It is the dot product of the magnetic field through the loop and the area of the enclosed loop. We can use the basic definition of magnetic flux to determine the unit.

Complete step-by-step answer:
Magnetic Flux is the surface integral of the normal components of magnetic field lines passing through a closed loop. We can define the magnetic field in the following way,
${{\phi }_{B}}=B.A=BA\cos \Theta $

Where,
${{\phi }_{B}}$ is the magnetic flux
$B$ is the magnetic field
$A$ is the area of the enclosed area
$\Theta $ is the angle between the magnetic field vector and area vector.
Hence, the fundamental unit of Magnetic Flux is Volt-seconds.
However, the SI unit of the magnetic flux is Weber (Wb).
It is a very important unit in electromagnetism and we often use this unit to express other quantities as well.

Magnetic flux depends on two quantities - Magnetic field and Area.
Both of these components are vector quantities. However, the magnetic flux only depends on the magnetic field lines which are perpendicular to the surface of the closed-loop (or along the area vector). It is a closed surface integration of all these magnetic field lines.

The equation we have mentioned above works for a fixed magnetic field. Otherwise, we have to use this formula.
${{\phi }_{B}}={{B}_{1}}.d{{A}_{1}}+{{B}_{2}}.d{{A}_{2}}+{{B}_{3}}.d{{A}_{3}}+...=\sum\nolimits_{all}{{{B}_{i}}.d{{A}_{i}}}$
Or, we can write it in the following way,
${{\phi }_{B}}=\oint\limits_{A}{B.dA}$
Here, we are using closed circle integration.
As we are using dot products, the magnetic flux is a scalar quantity.

Note:
When the magnetic field is along the area of the closed surface, the magnetic flux is 0. It happens because the angle between the area vector and the magnetic field vector is 90°.
Whereas, the magnetic flux is maximum when the angle between these vectors is 0°.