Question
Explain Magnetic flux with figure.
✓
Answer
• Magnetic Flux :
→Number of magnetic field lines passing perpendicularly through a surface kept in magnetic field is called Magnetic flux $\left(\phi_{ B }\right.$ ) linked with that surface.
→In figure (a), Magnetic flux passing through plane having area A placed in a uniform magnetic field $\vec{B}$ can be given as follows.
$\phi_{ B }=\overrightarrow{ B } \cdot \overrightarrow{ A }= BA \cos \theta$
Where, $\overrightarrow{ A }=$ Area Vector
which is shown perpendicular to plane.
$\theta$ is angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$
→Unit : W $b$ (weber) OR Tm²
→Dimensions : $M ^1 L^2 T^{-2} A^{-1}$
→As shown in figure (b), when $\vec{B}$ and $\vec{A}$ have different magnitudes and directions at different
parts of plane (when there is non-uniform magnetic field and curved surface), then magnetic flux passing through surface can be obtained in following manner :
$\begin{aligned}
\therefore \phi_{ B } & =\overrightarrow{ B }_1 \cdot d \overrightarrow{ A _1}+\overrightarrow{ B _2} \cdot d \overrightarrow{ A _2}+\ldots . . \\
& =\sum_{\text {all }} \overrightarrow{ B _i} \cdot d \overrightarrow{ A _i}
\end{aligned}$
It means summation of magnetic flux passing through all surface elements. Where $\overrightarrow{d A_i}$ is $i^{\text {th }}$ area element and $\overrightarrow{ B }_i$ magnetic field at area element $d \overrightarrow{ A _i}$.
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