Voltage and Energy and lack of directionality

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Discussion Overview

The discussion revolves around the concept of electric potential and its relationship to energy and force in the context of point charges. Participants explore how the voltage at a specific point remains the same under different charge configurations and the implications of this for the force experienced by a test charge.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant states that electric potential is the measure of energy per charge and questions why the voltage at point P is the same for different charge configurations.
  • Another participant confirms that the electric potential at point P is indeed the same whether there are two charges Q at points A and B or a single charge 2Q at A, emphasizing that potential energy depends on distance from the charge.
  • The second participant explains that while the voltage may be the same, the force acting on a test charge at P differs due to the gradient of the potential, which affects the force per unit charge.
  • Visual aids are referenced to illustrate the differences in voltage and gradient for the two scenarios, although the images themselves are not included in the discussion.
  • One participant expresses understanding and appreciation for the clarification provided.

Areas of Agreement / Disagreement

Participants generally agree on the concepts of electric potential and its implications for energy and force, but there is an underlying complexity regarding the relationship between voltage and force that remains nuanced and is not fully resolved.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the definitions of electric potential and force, nor does it explore the mathematical details that could clarify the gradient relationship further.

ninevolt
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To my understanding electric potential is the measure of energy per charge.
Now what I don't understand is that the voltage at the point P will be the same if there is a positive charge Q at A and a positive charge Q at B, or if there is a positive charge 2Q at A. I don't get how a test charge at point P should have the same amount of energy in both cases. Help.
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You are indeed correct that whether we have two equal charges, Q, at A and B; or a charge 2Q at A or B, the electric potential at P will be the same. It is important to emphasise that the electric potential is a measures of energy. Since the potential energy of a test charge only depends on the distance from a point charge, it isn't unreasonable that P should have the same potential energy in these two cases.

However, this does not mean that the force acting on a test charge at P would be the same. The force per unit charge at P is related to the gradient (or slope) of the potential at P, i.e. the force depends on how the voltage changes at P. So, although the value of the voltage might be the same at P, its slope may be different. Let me show you what I mean with a few plots.

This first image is when there are two equal charges, Q, located and A and B and shows the voltage (with zero at infinity).


The second is when there is a single charge, 2Q, located at A.


Notice that in both figures, you can choose any point along the line x=0, and the voltage will be equal. However, what is different is the gradient (or slope) of the voltage field. It is this that determines the force acting on a test charge. So whilst the force acting on a test charge is not the same in the two cases, the energy is.

Remember that the electric potential energy is the work done bringing a test charge from infinity, to a point in space. In this case, to a distance "r" from two charges of magnitude Q, or a distance "r" from a single charge of magnitude 2Q.

I hope that this helps.
 
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Well said.
 
Ok, that makes a lot of sense. Thank you
 

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