Question

The ratio of the forces between two charges placed at a certain distance apart in the air and by the same distance apart in a medium of dielectric constant K is ______.

Options

• 1 : K²

• K : 1

• K² : 1

• 1 : K

Answer 1

The ratio of the forces between two charges placed at a certain distance apart in the air and by the same distance apart in a medium of dielectric constant K is 1 : K.

Explanation:

According to Coulomb's law, the force between two point charges is given by: 

`F = 1/(4piin_0in_r) * (q1q2)/r^2`

where:

• ∈₀ = permittivity of free space.
• ∈_r = dielectric constant of the medium.

Force in Air: 

`F_a = 1/(4piin_0in_r) * (q1q2)/r^2`

Force in a Medium: 

`F_m = 1/(4piin_0in_r) *(q1q2)/r^2`

Ratio of Forces:

`(F_a)/(F_m) = in_r = K`

or `(F_m)/(F_a) = 1/K `