Capacitance ( getting started)

[yikes_physics]

Homework Statement

A spherical capacitor is made of two insulating spherical shells with different dielectric constants k1 and k2 situated between two spherical metallic shells and separated by a vacuum gap. Geometrical dimensions of the cross-section are as shown in figure 2. Calculate the capacitance of this system.

Homework Equations

C= Q/V(subscript ab) (couldnt figure out the formatting for subscripts :(

The Attempt at a Solution

I honestly have no idea on how to do this, so that is why i am not looking for help getting the answer, i would just like some help on where to start. Problems without numbers really throw me through a loop and i can usually get them when i get a little jump start.

i believe that i should begin by calculating the area of the insulating spheres with constants k1 and k2 and plug into the equation? or should i treat it as 1 spherical capacitor inside another? this gets 2 equations 4$$\pi\xi$$(r(sub b)r(sub a))/(r(sub b) - r(sub a)) and 4$$\pi\xi$$(r(sub d)r(sub c))/(r(sub d) - r(sub c)) and treat that as 1 big capacitor?

in this way i get 4$$\pi\xi$$(r(sub d)r(sub b))/(r(sub d) - r(sub b))...does this sound right or am i off in the wrong direction?

 

[learningphysics]

What are: 4(r(sub b)r(sub a))/(r(sub b) - r(sub a)) and 4(r(sub d)r(sub c))/(r(sub d) - r(sub c)) ?

Let the charge on the inside sphere be Q... assume Q>0. let the charge on the outside sphere be -Q.

calculate the voltage between the 2 spheres... first get the field using Gauss' law (you'll have two parts to get the field within each of the dielectrics)... then the integral of -E.dr going from the inner sphere to the outer... that gives the voltage between the 2.

Then C = |Q/V|.

 

[yikes_physics]

4(r(sub b)r(sub a))/(r(sub b) - r(sub a)) and 4(r(sub d)r(sub c))/(r(sub d) - r(sub c)) are the 2 little spherical capacitors made up of spheres with radii a and b for the first one and spheres with radii c and d for the second one. no numbers are given, i have to solve C in terms of the radii and the other variables...which is why i don't like these questions, lol.

ill give it another shot, and i appreciate your help in this matter.

take care

 

[learningphysics]

4(r(sub b)r(sub a))/(r(sub b) - r(sub a)) and 4(r(sub d)r(sub c))/(r(sub d) - r(sub c)) are the 2 little spherical capacitors made up of spheres with radii a and b for the first one and spheres with radii c and d for the second one. no numbers are given, i have to solve C in terms of the radii and the other variables...which is why i don't like these questions, lol.

ill give it another shot, and i appreciate your help in this matter.

take care

I forgot about the vacuum gap... so you have 3 sections to get the field for instead of 2 like I initially thought...