here flux is how much pass through that line element.
flux where is the line and is the unit vector showing the direction which is to the line .
(a) let
line element
lets consider any vector (dont need z-component as we are in x-y plane) which is to . then surely the unit vector
since is to , the scaler product
let the other component be where are some constant.
so, and
hence
total flux=
It is also very clear from the diagram that there is no pasing through the line segment. so only fair result is that flux should zero.
(b)
again let any vector which is to . then we have
let where is a constant
then and
unit vector
then total flux across the line,
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