- Write as if you are talking to someone else and showing them how to solve the problem, explaining when and why you do each step
- The basic goal here is two-fold (1) to make it easy for someone else looking at your work to identify what you are doing and why, and what mistakes you might have made and (2) force you to articulate in words how you solved the problem (writing is thinking, and this adds more scaffolding to the knowledge you’re creating in your brain.)
- Your solutions should include approximately as many words as equations.
- Whenever you create variable name for the sake of a problem (Theta, F12, a, etc) you should state what that means because it will not be the same for everyone- it may be helpful that a total of 9 points were saved by students on this last problem set whose math was different but did clarify with a diagram.
- Say a few leading words about your approach to solving the problem, e.g. “Taking coulomb’s law and integrating it for each differential piece of charge across the arc.”
- Write a few words about how you get from one equation to the next, e.g. “take the log of both sides”, “doing a Taylor series”, “assuming x is much larger than a”, etc
- Write the symbolic form of the equation before you substitute any values into it
- Show which values you plugged into the equation to get your final answer (my favorite way of doing this is actually putting the values and their units into parentheses in place of the variable names, but there are other ways.)
- Show how the units work out in your final answer. This is easier if you keep things symbolic as long as you can, and then only substitute in the values at the end of the problems. This is sometimes a pain in the arse in electromagnetism, but it will help you a lot if you get used to it. It doesn’t have to be strictly getting everything down to kg, m, and s, but it could be something like “ $kq^2/r^2$” is a force, so that means if you multiple that by a distance you get energy.”