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  • Consider a closed loop 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 =B_{1}dA_{1},B_{2}dA_{2} ….

Consider a closed loop 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 =B_{1}dA_{1},B_{2}dA_{2} …. Now if we choose two different surfaces S_{1} and S_{2} have C as their edge, would we get the same answer for flux? Justify your answer.

 

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Explanation:-

If we consider two different surfaces S1 and S2 bounded by the same loop C, the flux will be the same for both surfaces, provided that the magnetic field B satisfies Gauss's Law for Magnetism. The magnetic flux is the same as in S_{1} and S_{2} as magnetic field lines do not start anywhere in the space because of continuity. As the numbers of magnetic field lines passing through the circuit are the same, therefore the flux would be the same for both of them.

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