Relationship between electric potential and electric field

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Homework Help Overview

The discussion revolves around understanding the relationship between electric potential and electric fields, specifically focusing on the classification of functions as scalar or vector fields. Participants are exploring how to demonstrate these classifications in the context of given problems.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the definitions of scalar and vector fields and how to demonstrate that certain functions fit these definitions. Questions arise regarding the necessity of transformations and the methods for showing these properties.

Discussion Status

There is an ongoing exploration of the definitions and characteristics of scalar and vector fields. Some participants suggest that demonstrating the nature of the fields can be done through inspection rather than complex transformations. However, there is no explicit consensus on the best approach to take.

Contextual Notes

Participants are working within the constraints of specific homework problems, which may limit the information available for discussion. The nature of the functions in the problems is under scrutiny, particularly in terms of their classification as scalar or vector fields.

Flotensia
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Homework Statement


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Homework Equations

The Attempt at a Solution


I could find how to solve #2,4, but I don't understand what #1,3 need to me. How can I prove some functions are scalar field or vector field?
 
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Flotensia said:
How can I prove some functions are scalar field or vector field?
The first step would be to find out what scalar and vector fields are. Once you do that, the rest should be fairly obvious.
 
Scalar field means the function of points associating scalar value. Is it clear?Then should I do rotational transformation to prove?
 
I think you're trying to say that a scalar fields associates a scalar with each point in space, which is correct. So you have to show (show, not prove) that the potential does just that. You shouldn't need to go to the trouble of doing any transformations.
 
Don't we have to show the quantity of point is scalar or vector??
 
You can tell that by inspection. There is nothing but scalars in #1. In #3 the result is obviously a vector, since it is a gradient, which is a vector by definition.
 

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