Question

Define the curl & divergence of a vector..........also show the method to find both the quantities...........also define a solenoid vector using examples............(vector calculus)


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Answer 1

1) Divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, that is, a single number, while curl is itself a vector.

solenoid vector

2)In vector calculus a solenoidal vector field is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that the field has no sources or sinks. The field lines of a solenoidal field are either closed loops or end at infinity

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Answer 2

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field:

{\displaystyle \nabla \cdot \mathbf {v} =0.\,}

A common way of expressing this property is to say that the field has no sources or sinks. The field lines of a solenoidal field are either closed loops or end at infinity.