Introduction:
In this question, we are given two point charges and we need to find the magnitude of the electric field produced by each charge at the side of the other charge. We can determine the electric field by using Coulomb's law.

Coulomb's Law:
Coulomb's law states that the electric field produced by a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges. Mathematically, it can be expressed as:

F = k * (q1 * q2) / r^2

where F is the magnitude of the force between the charges, k is the electrostatic constant (9 × 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

Calculating the Electric Field:
To find the magnitude of the electric field produced by each charge at the side of the other charge, we need to consider one charge at a time and calculate the electric field produced by it.

Charge 1:
Let's consider charge 1 as the reference charge and calculate the electric field produced by it at the side of charge 2.

Step 1: Convert the distance between the charges to meters.
Given: Distance between the charges = 1.0 cm = 0.01 m

Step 2: Calculate the electric field produced by charge 1 at the side of charge 2.
Using Coulomb's law, we have:
Electric field (E1) = k * (q1 / r^2)

Substituting the values, we get:
E1 = (9 × 10^9 Nm^2/C^2) * (20 × 10^-7 C) / (0.01 m)^2

Simplifying the equation, we find:
E1 = 360 N/C

Charge 2:
Now, let's consider charge 2 as the reference charge and calculate the electric field produced by it at the side of charge 1.

Step 1: Convert the distance between the charges to meters.
Given: Distance between the charges = 1.0 cm = 0.01 m

Step 2: Calculate the electric field produced by charge 2 at the side of charge 1.
Using Coulomb's law, we have:
Electric field (E2) = k * (q2 / r^2)

Substituting the values, we get:
E2 = (9 × 10^9 Nm^2/C^2) * (20 × 10^-7 C) / (0.01 m)^2

Simplifying the equation, we find:
E2 = 360 N/C

Conclusion:
The magnitude of the electric field produced by each charge at the side of the other charge is 360 N/C.