- #1
Pushpam Singh
- 6
- 0
Please explain the relation between electric potential energy and electric field in detail.
Relation between electric potential energy and electric field
- Context: Undergrad
- Thread starter Pushpam Singh
- Start date
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Discussion Overview
The discussion focuses on the relationship between electric potential energy and electric field, exploring theoretical aspects and mathematical formulations. Participants examine the definitions and implications of electric potential and field in various contexts.
Discussion Character
- Technical explanation
- Mathematical reasoning
Main Points Raised
- One participant requests a detailed explanation of the relationship between electric potential energy and electric field.
- Another participant states that the component of the electric field at a point is equal to the negative gradient of the electric potential in that direction.
- A different participant discusses the condition ∇ x E = 0, suggesting that this allows the electric field to be expressed as a gradient of a scalar potential, leading to the equation E = -∇V. They note the importance of the choice of reference point in defining electric potential.
- One participant expresses disapproval of the initial question, directing others to a blog post for more information.
Areas of Agreement / Disagreement
The discussion includes multiple viewpoints regarding the relationship between electric potential and electric field, with no consensus reached on the best approach or explanation.
Contextual Notes
Participants mention the arbitrary choice of reference point in defining electric potential, which may affect interpretations of the relationship with electric field.
- #2
d.3vil
- 11
- 0
component of the electric field at
a given point in space is equal to minus the local gradient of the electric potential in that direction...
a given point in space is equal to minus the local gradient of the electric potential in that direction...
- #3
tannerbk
- 41
- 0
Because ∇ x E = 0, it is possible to write the electric field as a gradient of some scalar. This is true for any vector whose line integral around a close loop is 0 (path indepdendence). Because the line integral is path indepdendent we define V(r) = - ∫ E . dl . It is then easy to derive E = -∇V. I think these two equations provide the best insight into the relation between the electric field and the electric potential. Remember that in the definition of the electric potential there is a choice of reference point that is arbitrary. Thus any two V's differing only in reference point correspond to the same E.
- #4
mfb
Mentor
- 37,444
- 14,313
Please do not ask questions like that, see https://www.physicsforums.com/blog.php?b=3588 for details.
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