Question 26.5: If v = x²zi + 2y³z²j + xyz²k find div v....
If v = x²zi + 2y³z²j + xyz²k find div v.
Step-by-Step
Partially differentiating the first component of v w.r.t. x we find
{\frac{\partial v_{x}}{\partial x}}=2x zSimilarly,
{\frac{\partial v_{y}}{\partial y}}=6y^{2}z^{2} and {\frac{\partial v_{z}}{\partial z}}=2x y z
Adding these results we find
\mathrm{div}\,\mathbf{v}=\nabla\cdot\mathbf{v}=2x z+6y^{2}z^{2}+2x y z
Related Answered Questions
Question: 26.1
Verified Answer:
We find
{\frac{\partial{\bf{v}}}{\partial x...
Question: 26.2
Verified Answer:
\phi(x,y,z)=4x^{3}y\sin z
so that b...
Question: 26.3
Verified Answer:
(a) If Φ = x³y + xy² + 3y then
\frac{\parti...
Question: 26.4
Verified Answer:
Note that in this example F has only two component...
Question: 26.6
Verified Answer:
We have
v_{x}=x\sin y\, ...
Question: 26.7
Verified Answer:
\nabla \times v = \begin{vmatrix} i & j...
Question: 26.8
Verified Answer:
\nabla \times F = \begin{vmatrix} i & j...
Question: 26.9
Verified Answer:
\begin{array}{l}{{\nabla\phi=4x\mathbf{i}-2...
Question: 26.10
Verified Answer:
Given Φ = Φ (x, y, z) we have, by definition,
[lat...