Voltage Difference Equation Terminology

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Discussion Overview

The discussion revolves around the terminology and application of the voltage difference equation, specifically the limits of integration in the context of calculating voltage differences in a non-uniform charge density scenario. Participants explore the implications of choosing different limits and the conceptual understanding of voltage as a difference rather than an absolute value.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to determine the limits of integration in the voltage difference formula, asking whether to integrate from a to r or r to a when calculating voltage differences in a sphere with non-uniform charge density.
  • Another participant suggests that regardless of the chosen limits, the result will yield the same voltage difference, differing only by sign.
  • A further contribution emphasizes that voltage itself lacks physical meaning, and only voltage differences are meaningful, necessitating a reference point for calculations.
  • It is noted that the voltage difference can be expressed in terms of the limits of integration, showing that reversing the limits changes the sign of the result.
  • A participant references a convention regarding the expression of voltage differences, aligning with the established notation of Vb - Va.

Areas of Agreement / Disagreement

Participants express varying views on the interpretation of limits in the voltage difference equation, with some agreeing on the conceptual framework while others highlight the ambiguity in practical application. The discussion remains unresolved regarding the preferred approach to integration limits.

Contextual Notes

Participants acknowledge that the choice of limits affects the sign of the voltage difference, but there is no consensus on a definitive method for determining these limits in the context of non-uniform charge distributions.

Typhon4ever
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For the formula for getting voltage difference V_b-V_a=-\int _a^{b} Edl how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a? For example , in this question I am given a non uniform charge density where charge density increases with radius r for a sphere of radius a. Voltage is 0 at a. If I want to find the voltage difference between a point inside the sphere and a point on the surface of the sphere, what would I integrate from? -\int _a^{r} or -\int _r^{a}?
 
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Typhon4ever said:
For the formula for getting voltage difference V_b-V_a=-\int _a^{b} Edl how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a? For example , in this question I am given a non uniform charge density where charge density increases with radius r for a sphere of radius a. Voltage is 0 at a. If I want to find the voltage difference between a point inside the sphere and a point on the surface of the sphere, what would I integrate from? -\int _a^{r} or -\int _r^{a}?

Either way if you just want the difference- one way tells you how much lower a is than b, and the other way tells you how much higher b is than a. The result will be the same except for their sign.
 
Typhon4ever said:
For the formula for getting voltage difference V_b-V_a=-\int _a^{b} Edl how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a?
Remember that voltage doesn't have any physical meaning, only voltage differences do. So you always have to define your voltages as differences from some "reference" voltage. Your reference voltage is always a. The equation then gives you the voltage at b referenced to a. Note:
-\int_a^{a} E dl = 0 = V_a-V_a
So the voltage of any point referenced to itself is always 0, as you would expect.

Note also:
V_b-V_a= -\int _a^{b} Edl = -(-\int _b^{a} Edl) = -(V_a-V_b)
So the voltage of b referenced to a is the negative of the voltage of a referenced to b, as you would also expect.
 
As DaleSpam says, the voltage at b, referenced to a is conventionally given by Vb - Va
 
Thanks!
 

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