Find the divergence of the field F.
-$$F = - 3 x ^ { 4 } \mathbf { i } - 8 y ^ { 4 } \mathbf { j } + 6 z ^ { 4 } \mathbf { k }$$
A) $- 20$
B) $- 3 x ^ { 3 } - 8 y ^ { 3 } + 6 z ^ { 3 }$
C) $- 12 x ^ { 3 } - 32 y ^ { 3 } + 24 z ^ { 3 }$
D) 0

Question

Quizplus · Accepted Answer

The divergence of a vector field F is given by $
abla \cdot F = \frac{\partial F_{x}}{\partial x} + \frac{\partial F_{y}}{\partial y} + \frac{\partial F_{z}}{\partial z}$.

In this case, 
\begin{align*}
\frac{\partial F_{x}}{\partial x} &= -12x^3\
\frac{\partial F_{y}}{\partial y} &= -32y^3\
\frac{\partial F_{z}}{\partial z} &= 24z^3\
\end{align*}

Therefore, $
abla \cdot F = -12x^3 - 32y^3 + 24z^3$.

Hence, the best choice is (C).

Find the Divergence of the Field F F=−3x4i−8y4j+6z4kF = - 3 x ^ { 4 } \mathbf { i } - 8 y ^ { 4 } \mathbf { j } + 6 z ^ { 4 } \mathbf { k }F=−3x4i−8y4j+6z4k

Find the Divergence of the Field F $F = - 3 x ^ { 4 } \mathbf { i } - 8 y ^ { 4 } \mathbf { j } + 6 z ^ { 4 } \mathbf { k }$