What is the Electric Flux through a Small Disk near a Point Charge?

[ferret123]

Homework Statement

A small disc or radius R with surface normal
ˆ
k is placed a distance z from a point charge −q,( k hat pointing along the z-axis which goes through the charge and the center of the disk.)

Assuming that R ≪ z, derive an expression for the electric flux ΦE passing through
the disc.

Hint: Think of the correct approximation to make before starting the question.

Homework Equations

ΦE= q/ε

The Attempt at a Solution

I'm struggling to think of the approximation to simplify this problem. I can only think that with z much greater than R the disk would be a point charge but that wouldn't help at all. Any help to get started on the problem would be appreciated.

 

[haruspex]

Think about the area of the disc, and how that compares with an entire sphere radius z centred on the charge.