# Question based on capacitor

1. Jul 24, 2013

### sankalpmittal

1. The problem statement, all variables and given/known data
See the image:
http://postimg.org/image/q550yqqd1/ [Broken]

Left click to enlarge....

2. Relevant equations

For a parallel plate capacitor, Capacitance C=KεoA/d

A is area of plate and d is distance between the two plates..

3. The attempt at a solution

I do not know how to approach. I divided the capacitor along the diagonal into two halves. For the first half,

dC1 = K1εodA/dl

I took a strip of edge dx and length "l" perpendicular to the capacitor. Area of that strip= (x+dx)2-x2=2xdx..

dA=2xdx

Hence,
dC1 = 2K1εoxdx/dl

Now taking an angle θ, tanθ=d/a= (d-l)/(a-x)....

Am I going in the right direction ?

Last edited by a moderator: May 6, 2017
2. Jul 24, 2013

### Staff: Mentor

I can't clearly picture how you're dividing up the device. In my mind's eye I can see taking vertical slices of width dx across the image. At some horizontal position x, a slice will effectively consist of two capacitors in series, one with dielectric K1, the other with dielectric K2. "Plate" area is given by a*dx, and "plate" separation for each capacitor can be determined with a bit of geometry.

3. Jul 25, 2013

### sankalpmittal

Ok, So I have a differential form,

dC2=K2εoadx/distance, as per the hint you gave. I also understand that the two capacitors are in series. So what should I replace K with ?

And about geometry.... I took angle θ between diagonal and an edge. Then,

tanθ = d/a = y/x = (d-y)/(a-x)

where, the capacitor with dielectric constant K2 is positioned at distance x and its distance from the one edge(horizontal) to the boundary of second capacitor.

Am I on the right track ? Thanks..

4. Jul 25, 2013

### Staff: Mentor

I believe so... can you write expressions for the two capacitances of a slice?

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5. Jul 26, 2013

### sankalpmittal

gneill,

As per the image you gave,

Correct ?

Now dC=dC1*dC2/(dC2+dC1) ?

6. Jul 26, 2013

### Staff: Mentor

Right. You'll want to express d1 and d2 in terms of some common variable over which you can integrate.

7. Jul 27, 2013

### sankalpmittal

Ok, so replacing d2=d-d1,

Now, dC=dC1*dC2/(dC2+dC1)

Now to what limit shall I integrate this expression over ? Looks like I will have to eliminate d1.

By geometry, I got,

d(a-x)/a = d1

Correct ?

P.S. d is distance between plates as given. dC is small capacitance. dx is small distance between slices as per your image. (Thanks.)

Last edited: Jul 27, 2013
8. Jul 27, 2013

### Staff: Mentor

Sure. So you're integrating w.r.t. x. You should be able to see from the diagram the limits for x.

9. Jul 27, 2013

### sankalpmittal

Thanks a lot gneill !!!!

I integrated the expression in limits of x from zero to "a" and got the correct answer !! Thanks once again.