Since a long time I have been thinking of creating an encyclopedia of ignorance for the courses that I teach. When I correct papers, I see some standard mistakes students make.
Let me start randomly collecting them. May be some day I shall put them in order. I think I shall keep updating this page.
- The and field in an electromagnetic wave are point quantities. Text book diagram often makes people think about them as quantities extended in space.
- Density is also a point quantity which is defined as the ratio of mass ina volume to the volume, in the limit volume going to zero. Though theoretical such definitions are very useful practically.
- It is possible to have the function value zero at a point while its gradient is nonzero.Which also implies that the magnetic field at a point may be zero but the force on a dipole at that point may be nonzero.
- Keeping a body magnetically levitated does not require work.
- is not the same as , many student wrote this in their answers in the last exam. I tell them this would be like saying that usually makes sense to them.
- Over and over again I have to remind the students to try to make sense of the equations they write. For example while applying Lagrange’s mean value theorem to on students wrote, , replacing on the RHS by . The formula when simplified gives, which should raise a serious doubt, provided they stop doing mathematics mechanically and start thinking about meaning of the formulas.
- Exponential processes in a variable x can also be of the form , somehow many students think that only would be an exponential process but any given number can be written as hence can be expressed as .