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Consider a closed loop $\mathrm{C}$ in a magnetic field (figure). The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula $\phi=\mathrm{B}_1 \mathrm{dA}_1, \mathrm{~B}_2 \mathrm{dA}_2 \ldots$. . Now, if we choose two different surfaces $\mathrm{S}_1$ and $\mathrm{S}_2$ having $\mathrm{C}$ as their edge, would we get the same answer for flux. Justify your answer.
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The magnetic flux linked with the surface can considered as the number of magnetic field lines passing through the surface. So, let $\mathrm{d} \phi=\overrightarrow{\mathrm{B}} \vec{A}$ represents magnetic field lines in an area $\mathrm{A}$ to magnetic flux $\mathrm{B}$.
By the concept of continuity of lines B cannot end or start in space, so the number of lines passing through surface $\mathrm{S}_1$ must be the same as the number of magnetic lines passing through the surface $S_2$. So, in both the cases we gets the same magnetic flux.
By the concept of continuity of lines B cannot end or start in space, so the number of lines passing through surface $\mathrm{S}_1$ must be the same as the number of magnetic lines passing through the surface $S_2$. So, in both the cases we gets the same magnetic flux.
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