I organize and volunteer for a physics help study at my university. We get a range of students, including those just looking for quick answers and help on homework, those really looking for meaningful help in learning physics, and even those who love just hanging out to talk physics.
I don't mind that some students are there to only "get' quick help and aren't in it for some deep understanding. Most of the courses aren't structured in a way to help them learn. I am happy to guide them a long a little bit, and make them a little less frustrated by the crap they have to put up with. By helping them out (sometimes a little bit too much), I gain their trust and they actually get to learn something meaningful from time to time. Never underestimate trust.
This week, it seems, students have been learning about electric potential. They are assigned a lot of "exercises". I refuse to call them problems, because there is nothing problematic about them. Take for example, this problem, for which several students called me over to discuss.
The question just asked students to find the potential at a point in space due to three charges. The students had to do a bit of geometry to find some unknown lengths, but otherwise it was a simple straightforward calculation. Each of the student I met had correctly done the calculation. They had called me over because they had gotten the right answer that v= 0. These students must have been surprised by the answer, because they each called me over to discuss, "Does this make sense?"
OK. Stop. Hold the phones. Students spontaneously calling me over to talk about whether an answers makes sense. NOT, "do I have right answer?" NOT, "how do I do this?" They wanted to talk about whether or not an answer made sense.
And this is where I had to sigh. Because saying that the v =0 doesn't mean much. Really, you have to know what the potential is at nearby points to say anything. Because knowing differences in potential tells you something about electric fields and/or where charges are likely to move. Sure, sure, maybe you can make some argument about how it tells you that the potential there is the same as the potential at infinity. And then we can talk about how much net work it would take to bring in a particular from infinity. Sure, sure, sure. But what does v =0 mean? Not much.
So, here these students are, and they have been asked to do this "exercise" by performing some rote calculation using the formula k*q/r. They do it well. And they are puzzled? And I have to be the one to tell them that answer is meaningless, pretty much anyway. Not that their answers is meaningless, but that any answers would be meaningless. (Note: We did talk about why it was meaningless; and what else you would need to know for it be meaningful. But I digress)
Here's why I am so frustrated. We complain so much about students not stopping at the end of the problem to ask, 'Does this make sense?' But I'm the one who has to look them in the face and say, well, your professor has assigned you a problem that isn't about making sense of anything. He just wanted you to do some push-ups. I have to say that the best we can do is to check your work and make sure you calculated it correctly, and maybe to offer a mathematical explanation for why it seems plausible (based on geometry) that it could work out to zero. But I can't offer them an answer to the question, "Does it make sense?" from a physical sense without really twisting things around and bringing in a lot of baggage about potential energy, work, infinity, etc.
Am I wrong? Can I make meaning out of this stupid calculation students have been asked to do?