The solution says IF aA+bB=0, THEN a=b=0. That is what it means for the vectors A and B to be linearly independent. Vectors in a basis must be linearly independent.
You're using conservation of energy. Energy is not the only thing conserved in elastic collisions. In fact, the thing I'm thinking of is conserved even in inelastic collisions.
Did you forget to attach the picture? Maybe I'm just stupid and don't know how to find it. I would want to make sure I understand the question correctly. The integral in your "attempt" goes from -\phi to +\phi. That makes me think that the rod is only a semicircle when \phi = \pi / 2. I'm...
Looks good to me. So, when you combine the x and y components of the field using the Pythagorean theorem, you are effectively calculating the magnitude of the electric field. I don't think you need to do that, although you certainly can do. I would think it sufficient to say the x and y...
Where did you get this question? You cannot use Gauss' law in general to calculate the electric field unless you have some rather strong symmetries (usually planar, cylindrical, or spherical).
The electric quadrupole is an example of using the four charges in your question while producing a...