Prof. Dr. Christian Schuster
Technische Universität Hamburg-Harburg
Howto Solvean EM FieldProblem
Make sureyouunderstandtheproblem! Whatisbeingaskedfor?
Whatisthe"set up" of the problem (assumptions, number of dimensions, boundary conditions, …)?
What class of EM field behavior does the problem belong to (static, fully dynamic, …)?
What physical effects are possible at all?
Is there any sort of symmetry involved? If yes, can you take advantage of a coordinate transformation?
Even better, can you solve the problem by using Maxwell’s equations in integral form?
Can you solve the problem by using linear superposition of knownfields?
Can you solve the problem by using Green’s functions (Poisson/Coulomb integral, Biot-Savartlaw)?
Can you apply the method of image charges/currents?
Is the problem uncoupled or coupled in the variables (space and time)?
If uncoupled, can you solve by direct integration?
If coupled, does a separation of variables ansatzhelp?
Can you use analogies (e.g. analogy between Dand Jfields allows to calculate Rfrom C)?
Are media interfaces involved? If yes, ensure the boundary conditions are fulfilled!
Can you use "derived" equations (conservation of charge/energy, Fresnel’s formulas, …)?
Check the dimension of your final result! Is it correct? Does the result make sense physically?