Understanding on potential near a charge

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Discussion Overview

The discussion revolves around the concept of electric potential near charges, specifically examining the potential differences between points in the vicinity of positive and negative charges. Participants explore theoretical implications, definitions, and the nature of work done on or by test charges in electric fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question the sign of the potential difference between points P and Q, noting that while Vp - VQ is understood to be positive, the reasoning for VQ - VP being positive is unclear.
  • There is a discussion on the definition of electric potential, with some asserting that potential should be greater near the source charge, leading to confusion about the implications of the formula V = Q/4ε°r.
  • Participants express uncertainty about the representation of the figures, particularly regarding the arrows and their meaning in the context of electric fields.
  • Some argue that the work done on a test charge and the work done by a test charge should be considered differently, emphasizing that potential is a scalar quantity and direction may not matter in terms of potential magnitude.
  • There is a clarification that work done on the test charge is by an external agent, while work done by the test charge is due to the source charge's influence.
  • One participant suggests revisiting the relationship between work and energy in the electrostatic context, indicating that potential can be negative and that this does not necessarily imply direction.

Areas of Agreement / Disagreement

Participants express various viewpoints on the definitions and implications of electric potential and work done by test charges, indicating that there is no consensus on these concepts. Multiple competing views remain, particularly regarding the interpretation of potential differences and the nature of work in electric fields.

Contextual Notes

Some participants note limitations in the figures provided, such as the lack of units for charge or distance, which may affect the clarity of the discussion. Additionally, there are unresolved questions about the implications of potential being defined in relation to the work done against the electric field.

rajeshmarndi
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From the fig 1 & 2 in the attachment.

i) what is the sign of potential difference in fig.1 Vp – VQ
ii) And in fig.2 VQ – VP

For simplicity, let's take value at P,Q and R as in the figure(attach) for a unit +ve charge.

Both the answer are positive. I can understand i) is positive but not ii), as that means VQ > VP. I know this is what we get when we use the formulae V = Q/4ε°r. But my understanding near the source charge, the potential to do work should always be greater i.e Vp > VQ .

Electric potential at a place is defined as the potential of a unit +ve charge to do work when placed at that point and therefore point near the source would always have greater potential.What is wrong on my understanding?

Also, can't we take unit -ve charge as test charge, since it too has the same potential to do work as the unit +ve charge, only direction of work done is opposite.Thanks.
 

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rajeshmarndi said:
From the fig 1 & 2 in the attachment.
What is this supposed to be showing us? I am reading these as lines of charges without units for charge or distance given. I don't understand what the arrow is supposed to represent.
i) what is the sign of potential difference in fig.1 Vp – VQ
ii) And in fig.2 VQ – VP
If I take these points to be the locations of point charges than the PDs will be undefined.
For simplicity, let's take value at P,Q and R as in the figure(attach) for a unit +ve charge.

Both the answer are positive. I can understand i) is positive but not ii), as that means VQ > VP. I know this is what we get when we use the formulae V = Q/4ε°r. But my understanding near the source charge, the potential to do work should always be greater i.e Vp > VQ .
A +ve charge is attracted to a negative charge so you have to do work to take it away. Thus points close to a negative charge have a low potential compared with points a similar distance from the same strength positive charge.

The sign of the potential depends on your reference point.

Also, can't we take unit -ve charge as test charge, since it too has the same potential to do work as the unit +ve charge, only direction of work done is opposite.
Yes, that's quite valid ... the physics works out the same you just have to pay close attention to the signs. The shape of the potential vs space graph will just be upside down compared with the convention.
 
What is this supposed to be showing us? I am reading these as lines of charges without units for charge or distance given. I don't understand what the arrow is supposed to represent.
these arrows are line of electric field of +ve and -ve charge Q.
If I take these points to be the locations of point charges than the PDs will be undefined.
these are points where its potentials are Vp and Vq.
A +ve charge is attracted to a negative charge so you have to do work to take it away. Thus points close to a negative charge have a low potential compared with points a similar distance from the same strength positive charge.
This is where I am confused. Isn't the same work is done by the test charge if placed at that same point. That is same potential magnitude at same distance from the source. Only direction changes but since potential is a scalar quantity direction shouldn't matter.
 
Last edited:
these arrows are line of electric field of +ve and -ve charge Q.
Ah - so there is one charge indicated by the circles with the + and - sign respectively. Note: the letter Q is commonly used to denote a charge.

This is where I am confused. Isn't the same work is done by the test charge if placed at that same point. That is same potential magnitude at same distance from the source. Only direction changes but since potential is a scalar quantity direction shouldn't matter.

In one case work is done on the test charge and in the other work is done by the test charge. Direction matters because work is determined by the change in potential difference, not the magnitude of the potential.
 
I'm little confused with work done still.

Like when you say work is done ON THE TEST CHARGE - is this work done on the test charge BY AN EXTERNAL AGENT in pushing it against the electric field.

And work done BY THE TEST CHARGE - is this work done on the test charge DUE TO SOURCE CHARGE i.e either repellsion or attraction.
 
I think you need to re-examine the relationship between work and energy then revisit the electrostatic case.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html

The potential is defined as the work (per unit charge) done against the electric field. Thus changes with the field - in the direction the test charge wants to go by itself - would show up as negative.

Note: scalar's can be negative numbers. The negative sign does not have to mean direction.
 

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