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

question 56

Multiple Choice

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) \(f ( x , y , z ) = \frac { x + y } { z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } } } + C\)

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