Question

The dielectric constant $K$ of an insulator can be
A. $\mathrm{\infty }$
B. $$zero$$
C. $-2$
D. $6$

Answer 1

Hint: We know about Coulomb's law that the electrostatic force acting between two the point charges is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between these two charges. This force acts along the straight line joining the charges.

Complete step-by-step solution:
Formula for representation of coulomb’s law is as follow: $F={\displaystyle \frac{qQ}{4\pi {\epsilon }_0{r}^2}}$, where $r$ is the distance between the charges and $q,Q$ is the charges.
${\epsilon }_0$ is the permittivity of free space or vacuum permittivity i.e. always equals $1$.
If there any other medium is present between the point charges the permittivity is called the permittivity of the material. The dielectric constant is a relative quantity. it is the ratio of the permittivity of free space to the dielectric permittivity of the material.
$K={\displaystyle \frac{\epsilon }{{\epsilon }_0}}$ where $K$ is the dielectric constant of the material, $\epsilon$ is the permittivity of material presents in the medium between the point charges.
We know that the value of the dielectric constant for the free space or vacuum is always equal to $1$ and for insulators, it is always greater than or equal to $1$. In the given question only option D has the value greater than $1$ so the correct option is D.
The higher the value of the permittivity constant of the material lowers the force acting between the charges because the material present between them decreases the force of attraction or repulsion.

Note: The dielectric constant has the power to control the magnitude of force experienced by the charges. If the charges have the same nature, the force between them is repulsive, if they have different charges like one is negative and the other is positive then they attract each other.