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Consider a closed loop C in a magnetic f...

Consider a closed loop C in a magnetic field as shown in figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula `phi=vecB_1 . dvecA_1 + vecB_2 . dvecA_2`+…. Now if we choose two different surfaces `S_1` and `S_2` having C as their edge, would we get the same answer for flux. Justify your answer.

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Magnetic flux linked with any surface can also be determine by no. of field lines passing from it.

Here, from surface `S_1` and `S_2` no. of fieldline passing through them are same so flux linked with them is also same.
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