Problem with variable capacitor and changing angles

[lesdavies123]

Homework Statement

Here is the problem: A variable capacitor has seven armatures in the shape of half-circles with a radius of 2 cm. The armatures have a distance of 1 mm separating them. Find the capacity when the angle θ is: (a) 0 degrees; (b) 45 degrees; (c) 135 degrees.

Homework Equations

I guess relevant equations are C=Q/V and C=ε0 * A / d with d being the distance between the armatures. Also ε0 is the constant of permitivitty of empty space which is 8.85 x 10^-12 F/m.

The Attempt at a Solution

Basically, I've done problems with capacitors with two armatures, but now there are 7, so I don't know how they are paired up. Usually, the area obtained is the area of one of the two armatures, so here would the area be that of only one armature or should we multiply it by 3.5 to have half the total area (I tried that, but it didn't work). Also, I don't know how the angle changing would be reflected in any equations or what effect it would have. A little help to get me started would make me very happy. Thank you!

 

[rude man]

There are 7 rotating and 8 stationary semicircular plates. The effective area is the part covering both the stationary and rotating plates.

All rotating plates connect to each other. All stationary plates connect to each other.