Question

Define gradient, divergence and curl of a vector. Explain their physical significance.

Answer 1

In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.

Answer 2

Answer:

Gradient  and curl are vector quantity and divergence is scalar quantity .

Explanation:

Gradient : The gradient is a vector quantity that represents the derivative                       of a multivariable function. That is change in for all variables in a function. It is denoted by upside down delta.

Divergence :  The divergence is a scalar-valued function that takes in the vector-valued function that defines this vector field and outputs a scalar-valued function that measures the change in fluid density at every point.

  It is  a dot product of del with the vectors.

Curl : The curl is a vector operator in vector calculus that describes a vector field's infinitesimal circulation in three-dimensional Euclidean space. The curl at a given place in the field is represented by a vector whose length and direction correspond to the greatest circulation's magnitude and axis. Irrotational refers to a vector field with no curl.