Strangely aligned capacitor plates

[mateomy]

Working along step-by-step with a text and I'm stumped as to how they reached a conclusion. In the first picture you see two plates aligned at an unspecified angle, theta. One plate is at a potential V and the other is grounded. The distance between the plates at one end is d, and at the other end d+a. You can see in the second picture how they've set it up with respect to a two dimensional coordinate system. Maybe it's late and I'm braindead or maybe not in any even I can't see how they've formed the relationship between b,d and a to determine the distance between the actual origin and the intersection of the plates (dotted lines in picture three). Can anybody enlighten me?

Thanks.

 

[mateomy]

P.S. the whole point is to find the potential, but this is where I'm hung up.

 

[robphy]

In the triangle (in x<0) with base OO' and the height d, you have
tan(theta_0)=d/(OO').

In the trapezoid (in x>0), draw the horizontal at height d to form a similar triangle,
with base b and height a. Thus
tan(theta_0)=a/b.

 

[mateomy]

Truly geometry is my weakest link. Thank you.

 

[paranormal]

It is not uncommon to encounter difficulties when trying to understand complex scientific concepts, especially when working step-by-step with a text. It is possible that the explanation provided in the text may not be clear or may require further clarification. In situations like this, it is always helpful to seek assistance from a colleague or mentor who may have a better understanding of the topic.

Without seeing the specific pictures and equations mentioned in the content, it is difficult for me to provide a specific response. However, in general, the relationship between b, d, and a can be determined by using mathematical equations such as the Pythagorean theorem or trigonometric functions. It is also important to keep in mind that the distance between the plates may vary depending on the angle theta and the potential difference V.

In conclusion, it is always important to seek clarification and assistance when encountering difficulties in understanding scientific concepts. Collaborating with others and seeking help from more experienced individuals can greatly enhance our understanding and improve our problem-solving skills.