Find the potential function f for the field F.
-$$F = \frac { x } { z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } } } \mathbf { i } + \frac { y } { z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } } } j - \frac { 2 \sqrt { x ^ { 2 } + y ^ { 2 } } } { z ^ { 3 } } \mathbf { k }$$
A) $f ( x , y , z ) = \frac { \sqrt { x ^ { 2 } + y ^ { 2 } } } { z ^ { 2 } } + C$
B) $f ( x , y , z ) = \sqrt { x ^ { 2 } + y ^ { 2 } } + \ln z + C$
C) $f ( x , y , z ) = \frac { 1 } { z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } } } + C$
D) $f ( x , y , z ) = \frac { x + y } { z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } } } + C$

Question

Quizplus · Accepted Answer

The potential function $f(x, y, z)$ is found by integrating the components of the vector field $F$. The given vector field's components are naturally integrated to $f(x, y, z) = \frac{\sqrt{x^2 + y^2}}{z^2} + C$, which matches choice A.

Find the Potential Function F for the Field F A) f(x,y,z)=x2+y2z2+Cf ( x , y , z ) = \frac { \sqrt { x ^ { 2 } + y ^ { 2 } } } { z ^ { 2 } } + Cf(x,y,z)=z2x2+y2​​+C

Find the Potential Function F for the Field F A) $f ( x , y , z ) = \frac { \sqrt { x ^ { 2 } + y ^ { 2 } } } { z ^ { 2 } } + C$