Question

When air is replaced by a dielectric medium of force constant K, the maximum force of attraction between two charges, separate by a distance:
A). Decreases K times
B). Increases K times
C). Remains unchanged
D). Become $\dfrac {1} {{K}^{2}}$ times

Answer 1

Write the equation for the force of attraction between two charges in air and that in the dielectric medium. These two forces are directly proportional to each other. Thus, substitute the equation for the force of attraction in the air in the equation for the force of attraction in a dielectric medium. And then, get the force in the medium in terms of force in the air.
Formula used:
${F}_{a}=\dfrac {1}{4\pi {\epsilon}_{0}} \dfrac {{q}_{1}{q}_{2}}{{r}^{2}}$
${F}_{d}=\dfrac {1}{4\pi {\epsilon}_{0} K} \dfrac {{q}_{1}{q}_{2}}{{r}^{2}}$

Complete step-by-step solution:
Force of attraction in the air between two charges is given by,
${F}_{a}=\dfrac {1}{4\pi {\epsilon}_{0}} \dfrac {{q}_{1}{q}_{2}}{{r}^{2}}$...(1)
Force of attraction in a dielectric medium between two charges is given by,
${F}_{d}=\dfrac {1}{4\pi {\epsilon}_{0} K} \dfrac {{q}_{1}{q}_{2}}{{r}^{2}}$ ...(2)
Where, K is a dielectric constant
Substituting equation. (1) in equation. (2) we get,
${F}_{d}= \dfrac {{F}_{a}} {K}$
Thus, the force decreases by K-times when air is replaced by a dielectric medium.
Hence, the correct answer is an option. A i.e. decreases K times.
Additional Information:
Dielectric materials can be solids, liquids, or gases. Examples of solid dielectric material include porcelain, glass, etc. Examples of gaseous dielectric material include air, nitrogen, etc.

Note: K=${\epsilon}_{r} = \dfrac {\epsilon}{{\epsilon}_{0}}$
Where ${\epsilon}_{r}$ is the absolute permittivity
${\epsilon}_{0}$ is the permittivity of free space in Farads per meter
${\epsilon}$ is the permittivity of a medium Farads per meter
The dielectric constant is also related to capacitance. When air is replaced by a dielectric medium of constant K, then the capacitance increases K times.
A dielectric constant is a unitless quantity. It is a number without measurements.