Ncert Exercises & Solutions

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 $ϕ = {\vec{B}}_{1} . d {\vec{A}}_{1}, {\vec{B}}_{2} . d {\vec{A}}_{2}$ ...... . 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.

Hint: The flux depends on the no. of field lines passing through the surface area.

Step 1: The magnetic flux linked with the surface can be considered as the number of magnetic field lines passing through the surface. So, let

dϕ = BA

represents magnetic lines in area A to B.

Step 2: By the concept of continuity of lines, B cannot end or start in space, therefore the number of lines passing through the surface

S_{1}

must be the same as the number of lines passing through the surface

S_{2}

. Therefore, in both cases, we get the same answer for flux.

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