Dielectric Constant — Prelims Questions

A parallel plate capacitor has a capacitance $C_0$ in air. When a dielectric slab of dielectric constant $K$ and thickness $d/2$ is introduced into the capacitor, completely filling half the space between the plates (where $d$ is the plate separation), what is the new capacitance?

Two point charges $q_1$ and $q_2$ are placed at a distance $r$ apart in vacuum. The force between them is $F_0$. If a dielectric medium of dielectric constant $K=4$ is introduced between them, what will be the new force between the charges?

A parallel plate capacitor is charged by a battery and then disconnected. A dielectric slab of dielectric constant $K$ is then inserted to completely fill the space between the plates. Which of the following quantities will decrease?

A parallel plate capacitor has plates of area $A = 100,\text{cm}^2$ and separation $d = 1,\text{mm}$. It is filled with a dielectric material of dielectric constant $K=5$. What is the capacitance of this capacitor? (Given: $epsilon_0 = 8.85 \times 10^{-12},\text{F/m}$)

An electric field of $100,\text{V/m}$ exists in a region of space. If a dielectric material with a dielectric constant of $K=2.5$ is introduced into this region, what will be the magnitude of the electric field inside the dielectric?

Which of the following statements about the dielectric constant is INCORRECT?

A capacitor with air between its plates has a capacitance of $10,\text{pF}$. If the space between the plates is completely filled with a dielectric material, the capacitance increases to $60,\text{pF}$. What is the dielectric constant of the material?