A test charge (q=-5uC) lies between two positive charges: 3cm from a 2uC positive charge, and 2 cm from a 3uC positive charge. Find the force and direction (in newtons) on the test charge.

I know I have to use Coulomb's law:
so:

F = KQ/r^2 = 8.99e9*2e-6/.03^2
F = 8.99e9*3e-6/.02^2

But then I'm not sure how I use these to find the force on the test charge, and whether it it towards the 2uC or 3uC charge.

Any help is greatly appreciated!

Also I needed help finding the electric field at the position of the test charge!

You got Coulomb's law wrong. You need the product of the two charges in the numerator.

The test charge is attracted to both charges on opposite sides. For the net charge, you have to take the difference of the two forces.

To find the force on the test charge, you need to calculate the forces exerted on it by each of the positive charges separately and then add them up.

1. Force from the 2uC positive charge:
Using Coulomb's law, the formula for the force between two charges is given by F = (K * q1 * q2) / r^2, where F is the force, K is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Substituting the values for the 2uC positive charge (q1 = 2 x 10^-6 C) and the distance (r = 3 cm = 0.03 m) into the formula:
F1 = (8.99 x 10^9 Nm^2/C^2) * (-5 x 10^-6 C) * (2 x 10^-6 C) / (0.03 m)^2

2. Force from the 3uC positive charge:
Using the same formula as above, substituting the values for the 3uC positive charge (q1 = 3 x 10^-6 C) and the distance (r = 2 cm = 0.02 m) into the formula:
F2 = (8.99 x 10^9 Nm^2/C^2) * (-5 x 10^-6 C) * (3 x 10^-6 C) / (0.02 m)^2

Now, to find the total force, you need to add the forces together:
F_total = F1 + F2

Regarding the direction of the force, you need to consider the charges involved. Since the test charge is negative (-5 uC), it will be attracted to the positive charges, resulting in forces that are directed towards them. Therefore, the forces from both the 2uC positive charge and the 3uC positive charge will act on the test charge in the same direction.

Finally, substitute the values and calculate the total force:
F_total = F1 + F2

Hope this helps!