Question

A parallel-plate capacitor is constructed with circular plates of radius 5.10×10−2 m . The plates are separated by 0.23 mm , and the space between the plates is filled with a dielectric with dielectric constant κ. When the charge on the capacitor is 1.3 μC the potential difference between the plates is 1120 V . Part A Find the value of the dielectric constant, κ. Express your answer using two significant figures.

Answer 1

3.7

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

r = Radius =
`5.1* 10^(-2)\ m`

A = Area =
`\pi r^2`

V = Voltage = 1120 V

d = Distance of plate seperation = 0.23 mm

Charge is given by

`Q=CV\\\Rightarrow Q=(k\epsilon_0 A)/(d)* V\\\Rightarrow k=(Qd)/(\epsilon_0 AV)\\\Rightarrow k=(1.3* 10^(-6)* 0.23* 10^(-3))/(8.85* 10^(-12)* \pi (5.1* 10^(-2))^2* 1120)\\\Rightarrow k=3.69164\\\Rightarrow k=3.7`

The value of dielectric constant is 3.7