$A$ square of side $x \, m$ lies in the $x-y$ plane in a region where the magnetic field is given by $\vec B = B_0 (3\hat i + 4\hat j + 5\hat k ) \, T$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is:

  • A
    $5B_0x^2 \, Wb$
  • B
    $3B_0x^2 \, Wb$
  • C
    $2B_0x^2 \, Wb$
  • D
    $B_0x^2 \, Wb$

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Consider a closed loop $C$ in a magnetic field as shown in the figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula $\phi = \sum \vec{B}_i \cdot d\vec{A}_i$. Now,if we choose two different surfaces $S_1$ and $S_2$ having $C$ as their edge,would we get the same answer for the magnetic flux? Justify your answer.

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