To solve problems in electrodynamics, or generally in the natural sciences can be quite complex or even frustrating. Nevertheless we can try to efficiently subdivide our efforts and cut down a big problem into smaller ones that are much more easy to handle.
Main Problem Solving Strategy
- Read the problem thoroughly.
- Draw a schematic if possible.
- Understand the setup: What is going on? Is something moving and you have to find the force?
- Abstract the problem: What are known and unknown variables? How do you have to describe them mathematically, scalars, vectors, ...?
- Divide and conquer: Can you separate the problem into smaller sub-problems? Are the sub-problems connected to each other?
- Summarize your knowledge: To which subject(s) does the problem belong? What are the laws and equations governing the subject?
- Connect knowns and unknowns: Using the equations, can you relate the knowns and unknowns? Do you have to do this stepwise, i.e. solve for A, then B with another equation?
- Try to solve the problem: put it all together, solve for the unknowns and get some results.
- Question your solution: Is the electric field of a point charge really constant? Can the potential of a dipole have a term corresponding to a single charge?
- Enjoy yourself: Most of the problems in electrodynamics historically took years or decades to be solved and you just did it! Its time for a nice hot chocolate!
Sometimes, however, we simply cannot perform one or more points in this list for several reasons: maybe we are not completely sure about the basics or just temporarilly a little slow on the uptake. Then we have to "unravel the knot"!
Unravel the Knot!
- Calm down and don't blame yourself: Really, the problem took a long time to be solved. You have put a fair effort into the problem so you already learned a lot even if you do not realize it yet!
- Take a break: If you're stuck with something, a short break will give you time to change your perspective or simply grab that piece of sugar your brain desperately needs.
- Work together: In most cases this is not only much more fun but also far more efficient.
- Ask somebody: You have written down all you know about the subject, read through the lecture over and over again but you simply do not make progress? Maybe you can find some colleague that would be glad to help you out!
- Reproduce the solution to a similar problem: The techniques we have to use are often quite similar. The method of image charges for example can be used to find the electric fields for a metallic sphere subject to a point charge or if the charge is close to a grounded metallic corner.
And now: Have fun and a nice experience solving problems in electrodynamics!