Divergence Of Vector

Divergence of Vector:

We now derive the expression for the divergence of a vector. In this orthogonal curvilinear coordinates system (u₁, u₂, u₃) the unit vector can be expressed as

By the vector equation can be written as

Then the divergence of is

Example:

1. If f and g are continuously differentiable show that is a solenoidal.

Solution: A vector is solenoidal if To show that is solenoidal. First we show that can be expressed as curl of vector.

Operating divergence on this and using the identity