Solve Gauss' Law Problem: Electric Flux Hemisphere

[Rockstar47]

Hello, everyone. I hope that you can help me get started on one of the problems I have due this week.

Homework Statement

Find the electric flux through the hemisphere z = (square root of a^2 - x^2 - y^2).

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The Attempt at a Solution

I'm fairly certain I need Gauss' law to help solve this. I know that the law is defined by the Electric flux being equal to the integral of E dot dA. I'm a bit confused about where to start plugging and chugging. I also have t note that there is no charge given in the problem. How does this affect things? My initial impression is to just plant my (square root of a^2 - x^2 - y^2) into the integral and due the work for both dx and dy. This would be done assuming that z tells us that our dA is in that direction. Would this make sense?

 

[berkeman]

You need to define the vector E field in order to take the dot product and integrate it, right? Or else if it's a flat E field that enters the equatorial circle of the hemisphere, you can just integrate the 2-D integral over the equatorial disk.

 

[Rockstar47]

Thanks Berkeman. Yes, I believe I would need to do that, somehow...if I can determine how to set that up into the integral.

But...I have to wonder, since the problem specifically mentions that there is no charge, does that mean that there is no electric flux, either? Would it actually be zero...no charge, no flux?

Edit: There is an Electric field, however (apparently...was added to the problem later).
E = Eknot(1/square root of 2 i hat + 1/square root of 2 k hat).