Explanation:
When two charged bodies are brought near each other, they experience a force of attraction or repulsion due to their charges. This force is known as the electric force.

Initial Charge:
In this case, we have two equal metal balls, one charged to +10 units of electricity and the other charged to -20 units of electricity. The charges on the two balls are equal in magnitude but opposite in sign. Hence, they will experience a force of attraction towards each other.

Force Calculation:
The force between two charged objects is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Before contact, the magnitude of the force between the two balls can be calculated as:

F = k * q1 * q2 / r^2

where k is the Coulomb's constant, q1 and q2 are the charges on the balls and r is the distance between them.

Let us assume that the distance between the balls is d. Then,

F1 = k * 10 * (-20) / d^2
= -200k / d^2

After Contact:
When the two balls are brought in contact with each other, their charges get redistributed. This redistribution happens in such a way that the final charges on the two balls are equal and opposite. Hence, after contact, both balls will have a charge of -5 units of electricity.

When the two balls are separated again to the original distance, they will have charges of -5 units and -5 units. Using Coulomb's law, we can calculate the magnitude of the force between them as:

F2 = k * (-5) * (-5) / d^2
= 25k / d^2

Ratio of Forces:
The ratio of the magnitude of the force between the two balls before and after contact can be calculated as:

F1 / F2 = (-200k / d^2) / (25k / d^2)
= -8

Hence, the ratio of the magnitude of the force between the two balls before and after contact is -8.

Conclusion:
When two equal metal balls with opposite charges are brought in contact with each other, their charges get redistributed and they acquire the same charge. When they are separated again, the force between them decreases by a factor of 8.