Capacitor With A Dielectric

Step 1: Understanding the Concept:
This problem involves a parallel plate capacitor filled with a dielectric material. We need to find the dielectric constant (k) using the given physical quantities. The capacitance of a capacitor can be determined from its charge and voltage, and also from its physical dimensions and the dielectric material.

Step 2: Key Formula or Approach:
The capacitance of a capacitor is given by the ratio of charge to the potential difference :
For a parallel plate capacitor with a dielectric material, the capacitance is also given by:
where is the dielectric constant, is the permittivity of free space ( ), is the plate area, and is the separation between the plates.
By equating these two expressions for , we can solve for .

Step 3: Detailed Explanation:
Given data:
Plate area, .
Plate separation, .
Charge, .
Potential difference, .
Calculation:
First, calculate the capacitance from the charge and voltage:
Next, rearrange the formula for the parallel plate capacitor to solve for the dielectric constant :
Now, substitute the known values into this equation:

Step 4: Final Answer:
The calculated value of the dielectric constant is approximately 11.3.