Question

I a vector
v is solenoidal . then div
V is equal to:​

Answer 1

Step-by-step explanation:

An example of a solenoid field is the vector field V(x,y)=(y,−x). This vector field is ''swirly" in that when you plot a bunch of its vectors, it looks like a vortex. It is solenoid since

divV=∂∂x(y)+∂∂y(−x)=0.

The divergence being zero means that locally no field is being "created" at each point, much as is the case with this vector field. For real world examples of this, think of the magnetic field, B⃗ . One of Maxwell's Equations says that the magnetic field must be solenoid.

An irrotational vector field is, intuitively, irrotational. Take for example W(x,y)=(x,y). At each point, W is just a vector pointing away from the origin. When you plot a few of these vectors, you don't see swirly-ness, as is the case for V.