Effect of radius changes on electric fields and potential difference?

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Homework Help Overview

The discussion revolves around the effects of changes in radius on electric fields and electric potential, specifically examining the relationships defined by the formulas for electric potential (V = kQ/r) and electric field (E = kQ/r^2).

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the implications of radius changes on electric potential and electric fields, questioning how the scalar nature of potential contrasts with the vector nature of electric fields. There is an attempt to reconcile the mathematical relationships with physical intuition.

Discussion Status

Participants are actively engaging with the concepts, with some expressing realizations about the differences between scalar and vector quantities. There is an acknowledgment of the need for calculations to clarify the effects of radius changes, but no consensus has been reached on the implications.

Contextual Notes

There is an emphasis on understanding the mathematical relationships and their physical interpretations, with participants noting the importance of directionality in electric fields versus the magnitude in electric potential. The discussion is framed within the context of homework help, suggesting constraints on providing direct solutions.

mirandab17
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Hello!

Okay so I understand that electric potential:

V = kQ/r

...must be influenced by the radius doubling because it would make the potential energy half of what it originally was because of the proportionality law, v is proportional to 1/r.

With electric fields though, how can there possibly be no change? The formula is

E = kQ/r^2

...meaning if should be influenced as well?

The answer is c, btw.
 
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So do the math - calculate the field before and after the change in position.
Note: E is a vector.
 
Oh! Right!

Since E is a vector, and the distance and charges on both sides are equal, then they always simply cancel out to zero. Whereas with electric potential, a scalar quantity, it is not affected by direction, merely magnitude, in which case both are positive, so the radius change will definitely affect it.

Thanks bud!
 
No worries - that "Oh! Right!" feeling is what I was going for :)
 

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