Inferring charge via electric field properties

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SUMMARY

The discussion focuses on inferring the net charge of a charge distribution based on electric field measurements at two distances: 1.5m with a field strength of 282 N/C and 2m with a field strength of 119 N/C. The relationship between electric field strength and distance is explored, indicating that the field does not decrease as 1/r². Instead, participants suggest using the ratio of electric field strengths and distances to derive a more accurate model for the electric field's behavior. The equation E = kq/r² is referenced, along with the derivative E' = -2kq/r³ to analyze the change in the electric field.

PREREQUISITES
  • Understanding of electric field concepts and measurements
  • Familiarity with the equation E = kq/r²
  • Basic calculus, specifically differentiation
  • Ability to interpret graphical data and curves
NEXT STEPS
  • Study the mathematical derivation of electric field strength from point charges
  • Learn about electric field lines and their graphical representation
  • Explore the implications of the inverse square law in electrostatics
  • Investigate the relationship between electric field strength and charge distribution
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in understanding electric field behavior and charge inference techniques.

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Homework Statement



You are 1.5m from a charge distribution whose size is much less than 1m. You measure an electric field strength of 282 N/C. You move to a distance of 2m, and the field strength becomes 119 N/C. What is the net charge of the distribution? HINT: Don't try to calculate the charge. Determine instead how the field decreases with distance, and from that infer the charge.

Homework Equations



E = kq/r2

The Attempt at a Solution



Well the electric field strength doesn't fall off as 1/r2, because if we calculate q for 1.5m using simple substitution, then use that q at 2m, I don't get the electric field given.

How do I figure out the field? If I am thinking graphically, I have two points (1.5,282) (2,119) and I have to find a curve that crosses those two points, a curve that describes how the electric field falls off.

I think the problem I am having here is that I am rusty on the math. I have a feeling that it would help to differentiate E = kq/r2 to perhaps be able to describe how the field is changing:

E' = -2kq/r3 But I am not sure how to use the given points to help...

E2/E1 = 0.422
r2/r1 = 4/3

Any hints would be appreciated!
 
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