A charge of 6.0 mC is to be split into two parts that are then separated by 3.00 mm. What is the maximum possible magnitude of the electrostatic force between those two parts?

A charge of 6.0 mC is to be split into two parts that are then separated by 3.00 mm. What is the maximum possible magnitude of the electrostatic force between those two parts?

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To find the maximum possible magnitude of the electrostatic force between the two parts, you can apply Coulomb's Law. Coulomb's Law states that the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's break down the problem step by step:

Step 1: Identify the given information.
We have a charge of 6.0 mC (microcoulombs) that is split into two parts.

Step 2: Determine the charges of the two parts.
Since the charge is split into two parts, let's assume one part has a charge of Q1 and the other part has a charge of Q2. We can write the equation:
Q1 + Q2 = 6.0 mC

Step 3: Calculate the maximum possible electrostatic force.
Coulomb's Law can be expressed as:
F = k * |Q1 * Q2| / r^2

Where:
F is the electrostatic force
k is the electrostatic constant (approximately 9 x 10^9 N m²/C²)
|r| is the magnitude of the charges (since force is a scalar quantity)
r is the distance between the charges

In this case, we want to find the maximum possible force, which occurs when the charges have the same sign (either both positive or both negative). So, we can set Q1 = Q2 = 3.0 mC (half of the total charge). The distance between them is given as 3.00 mm, which we convert to meters: r = 3.00 mm = 0.003 m.

Now, substituting the values into Coulomb's Law:
F = k * |Q1 * Q2| / r^2
F = (9 x 10^9 N m²/C²) * |(3.0 x 10^-3 C) * (3.0 x 10^-3 C)| / (0.003 m)^2

Simplifying the equation, we get:
F = (9 x 10^9 N m²/C²) * (9 x 10^-9 C²) / (9 x 10^-6 m²)
F = 9 N

Therefore, the maximum possible magnitude of the electrostatic force between the two parts is 9 Newtons.