I have a presentation about these tommorow, and i have no idea how im gonna explain this to my class. please help…
Im an engineering student FYI
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Not sure how you expect this to be explained in 5-year-old terms, but roughly speaking:
An irrotational vector field is one where ∇ x F = 0 (i.e. no curl).
Intuitively this means that the field isn’t swirling or rotating. If you look at any little bit of the field nothing will be going around it. If you want it in terms of integration, if you take a small surface within the field, the total field going around the boundary of it will be 0 – nothing will be going around.
A solenoidal vector field is one where ∇ . F = 0 (i.e. no divergence).
Intuitively this means that the field has no sources or sinks. The field lines go in loops, rather than starting anywhere or stopping somewhere. This is the opposite of the irrotational ones – there is no in/out motion, only swirly motion. If you want it in terms of integration, given any bubble of space every field line that comes into the region must also leave it.
This assumes you understand what a vector field is.
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