I think a better way to sum up the discussion would be this: Physics degree does not provide direct training for any career, except academic. If you are not interested in that, you must be prepared to study/train more on top of your degree.
The concept of Physics serving as a filter reminds me of a joke that circulated in my grad school:
A graduate TA is teaching Physics to a bunch of pre-med students. In the middle, a student raises his hand:
"And why do we need to know all this?"
Without missing a beat, the TA replies...
Wait - it seems like you are using a Gauss law instead of Ampere's law. You need a circulation of B-field around the boundary of your surface. It will be proportional to the current going through the surface.
What angers me the most is it waters down the value of the degree. In fact, looking at the courses, I think you can graduate with a BS in Mathematics from my school and not do a single proof if you plan correctly; things like Topology, Algebra and Analysis can be avoided, and you'll still have...
Free body diagram for one of the wires is a great idea. You are right that veritical component of tension should be equal to the force of gravity and horizontal component is equal to magnetic force between the wires. This gives you two equations with two unknowns.