Find the Potential Function F for the Field F $$\mathbf { F } = - \frac { 1 } { x } \mathbf { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } - \frac { 1 } { \mathrm { z } } \mathbf { k }$$

question 22

Multiple Choice

Find the potential function f for the field F.
- $$\mathbf { F } = - \frac { 1 } { x } \mathbf { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } - \frac { 1 } { \mathrm { z } } \mathbf { k }$$

• A) \(f ( x , y , z ) = \frac { 1 } { x ^ { 2 } } - \frac { 1 } { y ^ { 2 } } + \frac { 1 } { z ^ { 2 } } + C\)
• B) \(f ( x , y , z ) = \ln ( y - x - z ) + C\)
• C) \(f ( x , y , z ) = \ln \left( \frac { y } { x z } \right) + C\)
• D) \(f ( x , y , z ) = \frac { 1 } { x ^ { 2 } y ^ { 2 } z ^ { 2 } } + C\)

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Definitions:

Confidence Interval

A selection of values, based on sample results, assumed to incorporate the value of an obscure population parameter.

Mean

The average value of a data set, calculated by adding up all the numbers in the set and then dividing by the count of the numbers.

Confidence Interval

A spectrum of values, from sample measurements, that is anticipated to capture the value of a hidden population parameter.

Standard Error

A statistical measure that describes the distribution of sample means around the population mean, indicating the accuracy of a sample mean as an estimate of the population mean.