Inclined parallel plate capacitor

[mertcan]

hi, I wonder that inclined plate capacitor formula is the formula in last picture I shared? I am not sure because there are not enough examples about that ?

 

[NFuller]

Is there a derivation before this? It would help since I'm not completely sure what assumptions the authors are making.

 

[mertcan]

Is there a derivation before this? It would help since I'm not completely sure what assumptions the authors are making.

Here is the total work here.
ALSO I have ANOTHER question : initially we are used to see parallel capacitor of which plates are perpendicular to horizontal plane ( A CAPACITOR LIKE RECTANGULAR ), but let's think a parallel capacitor of which plates make an SAME angle with horizontal plane ( A CAPACITOR LIKE PARALLELOGRAM ).
My question is : A CAPACITOR LIKE RECTANGULAR of which height is same with A CAPACITOR LIKE PARALLELOGRAM has same capacitance with CAPACITOR LIKE PARALLELOGRAM??

 

[NFuller]

My question is : A CAPACITOR LIKE RECTANGULAR of which height is same with A CAPACITOR LIKE PARALLELOGRAM has same capacitance with CAPACITOR LIKE PARALLELOGRAM??

Are you asking at what plate separation the capacitance of a normal parallel plate capacitor equals that of a capacitor with both plates at some common angle?

If so, then the two capacitors will approach the same value as the plate separation approaches zero.

hi, I wonder that inclined plate capacitor formula is the formula in last picture I shared? I am not sure because there are not enough examples about that ?

They appear to be using two approximations here $\text{tan}\alpha\approx\alpha$ and $z_{1}\approx z_{0}+x_{1}$ for small $\alpha$.

 

[mertcan]

Are you asking at what plate separation the capacitance of a normal parallel plate capacitor equals that of a capacitor with both plates at some common angle?

If so, then the two capacitors will approach the same value as the plate separation approaches zero.

Yes you are so close to my question but only the plate separation angle is important ? Are not the distance between plates and height of plates (or capacitor) important ? Should they are same also?

 

[mertcan]

@NFuller could you have a look at my last question for your last reply?

 

[NFuller]

Are not the distance between plates and height of plates (or capacitor) important ? Should they are same also?

Yes, as the plate separation increases, the capacitors will decrease their capacitance.