Answer:
Step-by-step explanation:
First, let's convert the force to SI units, since we'll need to use them in our calculation:
1 kgf = 9.81 N
The force between the charges is given by Coulomb's law:
F = k * q^2 / r^2
where F is the force, q is the charge, r is the distance between the charges, and k is Coulomb's constant:
k = 1 / (4πε0) = 8.99 x 10^9 N·m^2/C^2
where ε0 is the permittivity of free space.
We can use the given force and distance to solve for the value of q:
9.81 N = 8.99 x 10^9 N·m^2/C^2 * q^2 / (0.01 m)^2
Solving for q, we get:
q = ± 3.0 x 10^-6 C
The charges must have the same magnitude, so we take the positive value:
q = 3.0 x 10^-6 C
Now, if the charges are placed in a liquid with permittivity ε = 8ε0, the force between them will be:
F' = k * q^2 / (ε * r^2)
We want this force to be the same as before, so we can set it equal to 9.81 N and solve for q:
9.81 N = 8.99 x 10^9 N·m^2/C^2 * q^2 / (8ε0 * 0.01 m)^2
Solving for q, we get:
q = ± 6.0 x 10^-6 C
Again, we take the positive value since the charges have the same magnitude:
q = 6.0 x 10^-6 C
So the magnitude of the charges in the liquid is twice that in air.