find the force and the force direction of a 2x10^-6 C charge that is 3m west of a +5x10^-6 C charge (0.01 N west)

To find the force between two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2

Where:
F is the magnitude of the force between the charges,
k is the electrostatic constant (k = 8.99 x 10^9 N m^2 / C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.

Let's calculate the force using this formula.

Given:
|q1| = 2 x 10^-6 C (charge of the unknown charge)
|q2| = 5 x 10^-6 C (charge of the +5 x 10^-6 C charge)
r = 3m (distance between the charges)

Substituting the values into the formula:
F = (8.99 x 10^9 N m^2 / C^2) * ((2 x 10^-6 C) * (5 x 10^-6 C)) / (3m)^2

Calculating the force:
F = (8.99 x 10^9 N m^2 / C^2) * (10^-5 C^2) / 9 m^2
F = (8.99 x 10^9 N m^2 / C^2) / 9
F ≈ 9.99 x 10^8 N

So, the magnitude of the force between the two charges is approximately 9.99 x 10^8 N.

To determine the direction of the force, we need to consider the charges. Since the charges have opposite signs (one is positive, one is negative), the force between them will be attractive. Therefore, the force between the two charges will act from the positive charge (the +5 x 10^-6 C charge) towards the negative charge (the 2 x 10^-6 C charge).

In this case, the force is directed towards the west, as indicated in the question. So, the force acting on the 2 x 10^-6 C charge is 0.01 N west.