How many times should the value of each of two identical point charges be changed so that when immersed

How many times should the value of each of two identical point charges be changed so that when immersed in a liquid dielectric with a relative permittivity ε without changing the distance between the charges, the force of interaction between them does not change?

The force of interaction of charges outside the dielectric:

F1 = kq1 ^ 2 / R ^ 2 (1).

The force of interaction of charges placed in a dielectric with a dielectric constant:

F2 = kq2 ^ 2 / εR ^ 2 (2).

In (1) and (2) the designations are used:

k – coefficient of proportionality;

q1 is the magnitude of charges in vacuum (air);

q2 is the magnitude of the charges in the dielectric;

ε is the dielectric constant of the medium;

R is the distance between the centers of the charges.

The force of interaction of charges should not change, so we can write down the equality of the right-hand sides (1) and (2):

kq1 ^ 2 / R ^ 2 = kq2 ^ 2 / εR ^ 2 (2);

q1 ^ 2 = q2 ^ 2 / ε;

q2 = q1√ε.

Answer: each of the charges must be increased √ε times.