Question

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!

Answer 1

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

Answer 2

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.