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

Consider a closed loop C in a magnetic field, Fig. 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 chose two different surfaces `S_(1)` and `S_(2)` having C as their edge, would we get the same answer for flux. Justify your answer.

Text Solution

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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 `dphi=BA` represnets magnetic lines in an area A to B.
By the concept of continuity of lines B cannot end or start in space, therefore the number of lines passing through surface `S_1` must be the same as the number of lines passing through the surface `S_2`. Therefore, in both the cases we gets the same answer for flux.
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