Find the Potential Function F for the Field F A) $f ( x , y , z ) = - \frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } + C$

question 59

Multiple Choice

Find the potential function f for the field F.
- $$\mathbf { F } = - \left( \frac { \mathrm { x } } { \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } \right) ^ { 3 / 2 } } \right) \mathbf { i } - \left( \frac { \mathrm { y } } { \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } \right) ^ { 3 / 2 } } \right) \mathbf { j } - \left( \frac { \mathrm { z } } { \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } \right) ^ { 3 / 2 } } \right) \mathbf { k }$$

• A) \(f ( x , y , z ) = - \frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } + C\)
• B) \(f ( x , y , z ) = \frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } + C\)
• C) \(f ( x , y , z ) = \frac { 3 } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } + C\)
• D) \(f ( x , y , z ) = \frac { 2 } { 5 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 5 / 2 } } + C\)

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Definitions:

Cross Elasticity of Demand

A measure of how the quantity demanded of one good responds to a change in the price of another good.

Soft Drinks

Non-alcoholic beverages that are typically carbonated and contain various flavorings and sweeteners.

Cross Elasticity of Demand

A measure of the responsiveness of demand for a good to a change in the price of another good, showing the degree of substitutability or complementarity between them.

Positive

Characterized by or displaying affirmation, constructive attributes, or optimism; also in economics, indicating numbers or conditions above zero or in surplus.