Calculating the Force Between Two Electrons at a Distance of 2 Angstroms

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SUMMARY

The discussion centers on calculating the electrostatic force between two electrons positioned 2 Angstroms apart using Coulomb's law. The formula employed is F(r) = (q1*q2)/(4*(pi)*e*r²), where q1 and q2 represent the charge of the electrons (1.602E-19 C), e is the vacuum permittivity constant (8.854E-12 F/m), and r is the distance in meters (2E-10 m). Participants consistently arrive at a force of approximately 5.7666E-9 Newtons, while the textbook states an incorrect value of 7.1999E-9 Newtons, indicating a potential error in the textbook.

PREREQUISITES
  • Understanding of Coulomb's law and electrostatic force calculations
  • Familiarity with fundamental constants such as the charge of an electron and vacuum permittivity
  • Basic knowledge of unit conversions, particularly Angstroms to meters
  • Proficiency in mathematical operations involving scientific notation
NEXT STEPS
  • Review the derivation and applications of Coulomb's law in electrostatics
  • Explore the implications of using Coulomb's constant (k = 8.99 x 10^9 N m²/C²) in calculations
  • Investigate common errors in textbook problems related to electrostatics
  • Learn about the significance of precision in scientific calculations and unit conversions
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Students in physics, educators teaching electrostatics, and anyone involved in scientific calculations related to forces between charged particles.

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Okay so I'm working on a question for practice and I'm sure I'm getting the right answer but the answer they give me is something different. Anyway the exact question is:

An electron is located at the origin of the coordinates, and a second electron is brought to a position 2 Angstroms from the origin. Calculate the force between the two electrons.

I'm guessing I need to use the equation:

F(r) = (q1*q2)/(4*(pi)*e*r2)

Where q1 and q2 are the magnitude of the charge of the electrons, which I'm taking to be e2 or (1.602E-19)2

Where pi is pi, ie 3.14159...etc

Where e is the vacuum permittivity constant, 8.854E-12

Where r is the distance between the two electrons in meters which I'm taking to be 2E-10 since 1 angstrom is 10-10 meters

Anyways I do the calculations and I'm getting 5.7666E-9 Newtons but in the back of the problem book it says the answer is 7.1999E-9 Newtons

It's close but I'm wondering if there's some trick to the problem or something I missed. Can someone confirm or dispute if I'm doing this correctly?
 
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I get 5.75. Used Coulomb's constant k = 8.99 x 10^9 instead of your 4*pi*ε.
 
Delphi51 said:
I get 5.75. Used Coulomb's constant k = 8.99 x 10^9 instead of your 4*pi*ε.

both k and 1/4*pi*ε are same ...

and i am also getting same answer i.e. 5.76 nN
so it seems the book is wrong somewhere
 
same answer here.
 
Well I entered the question exactly as it appears in the book so if we're all getting a different answer I guess it is just a problem with the book. Let's hear it for crummy 137$ textbooks.
 
sue the writer :smile:
 

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