The space between the two coaxial cylindrical shells of radius `R_(1)andR_(2)(R_(1)ltR_(2))` is filled by a dielectric substance, whose dielectric constant varies with the distance from the axis as `k=A//r^(3)`. If the length of the cylindrical shells is `l` then find the capacitance of the system

Explanation

To find the capacitance of the coaxial cylindrical shells filled with a dielectric whose dielectric constant varies with distance, we follow these steps:

### Step 1: Understand the Geometry and Variables
We have two coaxial cylindrical shells with inner radius \( R_1 \) and outer radius \( R_2 \). The dielectric constant \( k \) varies with distance \( r \) from the axis as \( k = \frac{A}{r^3} \), where \( A \) is a constant.

### Step 2: Electric Field Calculation
The electric field \( E \) between the two cylindrical shells can be derived from Gauss's law. The electric field in the region between the cylinders is given by:
\[
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