[Eternal Student (OP)]

Hi.

DECLARATION:   This is a homework question from a Physics book.   It's not my homework, I'm trying to help someone else but wouldn't want to advise them badly.   The minor issue is that I never studied electronics beyond school and I'm just going about this with some concepts of electrostatics.

    I'm looking for ideas on how to calculate the capacitance of the following object:

Two conductive plates of size   2cm x 1cm    ( x-axis length   by   y-axis length)    but there's a step in the thickness (z-axis measurement) of the plates at the location  x-axis = 1 cm.   The plates are separated with an air gap of  1mm   at one end   and   3mm at the other end.   See the diagram below.   Note the different units of measurement:   Lengths in centimetres but gaps in millimetres.

This is what I was going to suggest they did:
  One approach is to cut the diagram in half, consider it as two different capacitors each capacitor being a pair of conventional rectangular plates   1cm x 1cm.   
  The first capacitor having a gap of 1mm and the second having a gap of 3mm.    Use the usual estimate for parallel plates:   Capacitance, C =  ε . A/d.     Then find the total capacitance as usual   C  = C₁  + C₂ .     These (conceptually cut apart) capacitors are at the same voltage since the plates were a conductive material, so the conceptually separated capacitors are effectively connected in parallel .   
    Is that going to be a reasonable approximation, or does someone else have a better idea?
    This is a 5 mark question, so really shouldn't take more than 10 minutes under any circumstances.

Best Wishes.

[alancalverd]

Looks like a perfect solution to me.

[vhfpmr]

The quick way is to calculate the capacitance of the wide end, then either triple it if the spacing is 2mm as in the diagram, or quadruple it if the spacing is 3mm as in the text.

[Eternal Student (OP)]

Hi.
@vhfpmr
Thanks.   Sorry it's taken me a while to notice there was another reply. 
There is some disagreement between the text  (3mm)  and the diagram (2mm), that's my fault, I can't really recall which way it was supposed to be.     Your quick calculation is ok, it works.

Best Wishes.