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A long string with a charge of lambda pe...

A long string with a charge of `lambda` per unit length passes through an imaginary cube of edge `a`. The maximum flux of the electric field through the cube will be

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Maximum flux means maximum charge enclosed. Here the source of charge is a line charge distribution so we have to look for the maximum length into which the line charge can be accommodated. Note that the maximum length into which the line charge can be accommodated. Note that the maximum length in a cube is the largest diagonal which is `sqrt(3)a` (where a is the length of the side of the cube). So the maximum charge that can be accommodated in the cube is `sqrt(3)a lambda`.
Now, as per Gauss.s law, the maximum flux is `(1)/(epsilon_(0))` times the maximum charge included in the cube.
So, the maximum flux `=(sqrt(3)a lambda)/(epsilon_(0))`
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