Is electric field radially inwards or outwards

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Discussion Overview

The discussion centers on the direction of electric fields, particularly in relation to electric potential. Participants explore how to determine whether the electric field points radially inwards or outwards based on the relationship between electric potential and distance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how to determine the direction of an electric field, referencing specific problems from an external source.
  • Another participant explains that the electric field vector, ##\vec E##, points in the direction where the electric potential (V) decreases most rapidly, depending on the derivative of V with respect to distance (r).
  • A participant notes that the force on a positively charged test particle aligns with the electric field direction, while for a negatively charged particle, it is opposite, emphasizing the importance of careful sign usage in calculations.
  • One participant describes the notation used to represent electric fields in diagrams, indicating that an "x" symbol denotes the field going into the page and another symbol indicates it coming out of the page.
  • A later reply reiterates the notation and suggests that describing the electric field in terms of potential is preferable, referencing the relationship E = -∇V and the analogy of a positively charged object rolling down a potential gradient.

Areas of Agreement / Disagreement

Participants express varying perspectives on how to visualize and calculate the direction of electric fields, with no consensus reached on a definitive method or interpretation.

Contextual Notes

Some discussions involve assumptions about the nature of electric potential and its relationship to electric fields, which may not be universally agreed upon. The use of symbols in diagrams is also subject to interpretation based on context.

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In general, ##\vec E## points in the direction that V decreases most rapidly.

In this case, V depends only on r, so ##\vec E## points outwards if V decreases with increasing r (i.e. dV/dr < 0), and inwards if V increases with increasing r (dV/dr > 0).
 
The force on a positively charged test particle is in the direction of the electric field; the force on a negatively charged test particle is opposite to the direction of the electric field. If you're careful with your signs, you'll get the right answer just from doing the calculation because you'll write a negative charge as ##-Q## and the negative sign carries through into the sign of the force - but wise people also take a moment to visualize the setup and make sure that their answer has the force pointing in a sensible direction.
 
Alright man so what the symbols mean are: if it is the "x" symbol it means the field is going into the page (away from you) and if it is the other symbol then it means the field is coming out of the page (at you)
 
Sorthal said:
Alright man so what the symbols mean are: if it is the "x" symbol it means the field is going into the page (away from you) and if it is the other symbol then it means the field is coming out of the page (at you)

It is better to describe the Field in terms of the Potential - that avoids having to think of a 'page' or where you (or I) happen to be standing. Basically:
E = -∇V or the gradient of the Potential. It's the way that a positively charged 'ball' would 'roll', as jibell was hinting.
 

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