Coulomb's Law
force=k*q1*q2/r^2
applies only to two point charges (or two spherically symmetric distributions).
So, you can't use that as you have suggested.
Instead of a semicircle of continuously-distributed charge, imagine, say, 5 point-clumps of charge arranged symmetrically along the semicircle. Let's model this by dividing the semicircle into 5 identically sized pieces... then collapsing to the center of each piece. Since the 12 uC charge is not distributed evenly (according to the varying charge density.. that is, charge per unit length), some clumps have more charge than others... the total being 12uC, of course. Note that each point-clump contributes a force vector on the 3uC charge. Here, you can use the formula above because we have point charges. (Remember that the net force is a vector sum! By taking advantage of symmetry, the vector sum is a little simpler to calculate. Draw some force vectors with some care to see this.)
Unfortunately, this isn't the answer... only an approximation to the answer. You get a better answer by using, say, 9 smaller clumps... then taking the vector sum. Even better with 99 even-smaller clumps.. then taking the vector sum. Of course, the best answer comes from using infinitesimal (i.e. teeny-tiny) pieces and doing an vector integral (sum).
So, after appreciating the discussion above, you need to write down the appropriate integral. To get you started think about this: how much charge is contained in a teeny-tiny piece of arc of length "ds" at a given angle theta? You may want to express the teeny-tiny piece of arc length "ds" in terms of the teeny-tiny angle "dtheta". Once you have that charge, you can use Coulomb's law for the force due to that bit of charge. Do the same for each bit of charge, then add them up (integrate).
