# In some medium at a distance of 5 cm from a point charge of 0.45 μC

**In some medium at a distance of 5 cm from a point charge of 0.45 μC, the field strength is 20 kN / C. Determine the dielectric constant of the medium.**

Let’s write down a short statement of the problem:

r = 5 cm = 0.05 m.

q = 0.45 μC = 0.45 * 10 ^ (- 6) Cl.

E = 20 kN / Cl = 20,000 N / Cl.

It is necessary to find the dielectric constant of the medium ε.

The strength of the electric field created by the charge q is found by the formula E = F / q, where q is a point charge creating an electric field, and F is the force with which any charge introduced into this field at a point with a known strength will interact. This force is determined by Coulomb’s law. If the expression of force is substituted into the formula for tension, we get:

E = k * q / (ε * r ^ 2), where k = 9 * 10 ^ 9 H * m ^ 2 / Kl ^ 2. Hence ε = k * q / (E * r ^ 2)

Let’s make the substitution and calculations:

ε = (9 * 10 ^ 9 N * m ^ 2 / Kl ^ 2 * 0.45 * 10 ^ (- 6) Kl) / (20,000 N / Kl * (0.05 m) ^ 2)) = 81.

Answer: ε = 81.