#### Question

A sphercial capacitor is made of two conducting spherical shells of radii *a* and *b*. The space between the shells is filled with a dielectric of dielectric constant *K* up to a radius *c* as shown in figure . Calculate the capacitance.

#### Solution

We have two capacitors: one made by the shells a and c and the other made by the shells b and c.

The capacitance of the capacitor `C_(ac)` is given by

`C_(ac) = (4pi∈_0acK)/((c-a))`

The capacitance of the capacitor `C_(cb)` is given by

`C_(cb) = (4pi∈_0bcK)/(K(b-c)`

The two capacitors are in series; thus, the equivalent capacitance is given by

`1/C = 1/C_(ac) + 1/C_(cb)`

⇒ `1/C = ((c-a))/(4pi∈_0acK) + ((b-c))/(4pi∈_0cb)`

⇒ `1/C = (b(c-a)+Ka(b-c))/(K4pi∈_0abc)`

⇒ `C = (K4pi∈_0abc)/(b(c-a)+Ka(b-c))`

Is there an error in this question or solution?

Solution A Sphercial Capacitor is Made of Two Conducting Spherical Shells of Radii a and B. the Space Between the Shells is Filled with a Dielectric of Dielectric Constant Concept: Capacitors and Capacitance.