Total electric flux through a cube of side length L

I’ve just completed a question, question 7 on the attached sheet but I’m not convinced it is correct:( I was hoping someone could help me point out any errors in my work

Below I have posted both a photograph of the question (7) as diagrams are involved and figured it would be easier to take a photograph of my work to as it would be far too long to type:)

Attachment 68677

Attachment 68678

I hope it is clear to see what I have done in my working, it’s quite basic anyways but just incase……..

I first noticed that the only contributing flux would be that out of either side on the plane the positive and negative z direction, I then noticed that the plane was fixed on the z axis!

I then found the electric field of this square plane and having the electric field integrated from 0-L for the x and y components using gauss law:)

The only equations I used were that of Gauss, which are also on the working sheet

Apologies if the writing is unclear or my questions is unclear, I hope you can help it would be much appreciated 🙂

Thanks in advanced

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