Fitting Power Function to Graph Potential vs Distance: What is n?

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Discussion Overview

The discussion revolves around fitting a power function to a graph of electric potential versus distance, specifically exploring the exponent 'n' in the function F(r)=Ar^n. Participants are examining the relationship between potential and distance, considering both theoretical implications and practical data fitting.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks guidance on fitting a power function to their data and understanding what 'n' represents.
  • Another participant explains that 'n' is the exponent in the power function and can take various values, affecting the nature of the relationship (linear, quadratic, etc.).
  • A participant shares their data and the result of a trendline fit from Excel, indicating that the fit yields n = -2.011, suggesting a non-linear relationship.
  • There is a discussion about the implications of n being anything other than 1, which indicates a non-linear relationship, and whether the fit appears to be good.
  • One participant expresses confusion regarding the expectation of linearity and clarifies their understanding of the relationship between potential and distance, referencing a known equation V=kQ/r.
  • A participant inquires about calculating an experimental value for 'n' and its relevance to percent error calculations.
  • There is a question about whether the slope of the trendline corresponds to the constant value k, with a participant noting a slope close to a known value of k.

Areas of Agreement / Disagreement

Participants generally agree that 'n' is not expected to be 1 due to the non-linear nature of the data. However, there is no consensus on how to calculate 'n' or the implications of the slope of the trendline in relation to the constant k.

Contextual Notes

Participants express uncertainty about the best method to determine 'n' and how to compute percent error, indicating potential limitations in their understanding of the fitting process and its implications.

Who May Find This Useful

This discussion may be useful for students or individuals interested in data fitting techniques, power laws in physics, and the relationship between electric potential and distance.

dapavelko
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I am graphing Potential(Volts) y-axis vs distance (r) x axis. I am asked to fit a power function F(r)=Ar^n . Any ideas on how to do this? What is n supposed to represent?
 
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Hi dapaveko, welcome to PF!

EDIT: 'n' is just some number (any number).

'n' is the power (the exponent). 'n' could be 1, or 2, or 3, or 4, or...

in which case the function would be linear, or quadratic, or cubic, or quartic, or ...

The point is that it's some sort of power law. What you get as a result for 'n' depends upon what exponent produces a curve that best fits your data. (I am assuming that you are trying to fit a power law function to some data. Otherwise your question doesn't make much sense).
 
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r V
1 8.7
2 4.5
3 2.9
4 2.2
5 1.8
6 1.5

that is my data I got, and I made an excel. I added a trendline curved and got y=8.7715x^-2.011. The data was curved not linear? I am trying to associate the power function F(r)=Ar^n and determine n. Wouldn't n be the -2.011? Sorry your answer confused me so I added the data.
 


dapavelko said:
r V
1 8.7
2 4.5
3 2.9
4 2.2
5 1.8
6 1.5

that is my data I got, and I made an excel. I added a trendline curved and got y=8.7715x^-2.011.

Okay.

dapavelko said:
The data was curved not linear?

Are you asking me or telling me? Obviously if n is anything other than 1, then the data will not be linear. What were you expecting it to be like? Are the data curved? Does your fit look like a good fit?

dapavelko said:
I am trying to associate the power function F(r)=Ar^n and determine n. Wouldn't n be the -2.011?

Yes, of course. Excel has determined that n = -2.011 for you.

By the way, I edited my first post slightly.

dapavelko said:
Sorry your answer confused me so I added the data.

What, specifically, about it confused you?
 


ok I reread your post and I thought you were telling me it should be linear.

The question I am asked is...What I would expect "n" to be. Well I would expect it to be other than 1 because it is not a linear relationship ,the potential difference decreases with the first power of the distance. such as V=kQ/r

but is there a way I can calculate an n value? as I need to compute percent error and I need to find an actual value being the experimental value is given by excel?

Thanks for the help I think I was trying to make more out of what I was being asked.
 
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also would the slope of the trend-line represent the constant value k? I plotted both V to r and and also the magnitude of E to R and I get a slope of aprox... 8.77 which seems close to the k value of 8.99*10^9 ?
 
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