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Irrotational,rotational,solenoidal vecter field

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Q: What are rotational and irrotational fields?
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What do you understand by rotational and irrotational fields?

Irrotational fields are conservative, simply connected (path independent), and have no curl (del cross the field) = 0Rotational fields are orthogonal MTM=I, symmetrical, representable in any finite dimension through orthogonal matrix multiplication


What is vorticity for irrotational flow?

Zero


Is every irrotational vector field conservative?

No, for example (-yi +xj)/(x^2 + y^2) is irrotational but not conservative on the domain {(x,y}|x^2 + y^2 > 0}.


Why do people do rotational farming?

Because farming certain plants drains certain nutrients from the soil. Rotational farming rotates the crops being grown (sometimes fields are left fallow i.e. empty) and therefore, nutrients remain in the soil.


How torque is developed due to alignment of two fields?

Torque is developed by, among other things as well, the magnetic attraction or repulsion of two magnetic fields, contributing through rotational leverage to produce a net torque.


How do the orientations of Uranus' and Neptune's magnetic axes differ from those of the other planets?

The magnetic fields are not aligned with the rotational axis of the planet and they are not located at the center of the planet.


What are the rotational symmetries of a heart?

a heart have no rotational symmetry!


What is the rotational symmetry of a trapezoid?

A trapezium does not have rotational symmetry.


How many rotational symmetries does a octagon have?

It has 8 rotational symmetry.


How much rotational symmetry does an octagon have?

It has 8lines of rotational symmetry


What is the rotational symmetry of a rectangle?

It has rotational symmetry to the order of 2


Which triangles have rotational symmetry?

Equilateral triangles have rotational symmetry.