Two Electrons and Distance Equation

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SUMMARY

The discussion centers on calculating the distance between two electrons, where one electron is released above the Earth's surface and the other is positioned directly below it. The gravitational force acting on the first electron, calculated using F=ma, is balanced by the electrostatic force exerted by the second electron, described by F=kq1q2/r^2. By equating these two forces, the distance can be determined by rearranging the formulas and substituting the known values for mass, charge, and gravitational acceleration.

PREREQUISITES
  • Understanding of Newton's laws of motion (F=ma)
  • Familiarity with Coulomb's law (F=kq1q2/r^2)
  • Basic knowledge of electrostatics (charge and force relationships)
  • Ability to perform algebraic manipulations and calculations
NEXT STEPS
  • Study the derivation of Coulomb's law and its applications in electrostatics
  • Learn about gravitational force calculations and their implications in physics
  • Explore the concept of electric fields and their relationship with force
  • Practice solving problems involving multiple forces acting on a single object
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Students in physics, particularly those studying electromagnetism and mechanics, as well as educators looking for problem-solving strategies in electrostatics and gravitational interactions.

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An electron (mass of 9.110×10-31kg and charge of -1.602×10-19C) is released at rest above the surface of the Earth (where g = 9.81 m/s2). A second electron directly below it exerts an electrostatic force on the first electron that exactly cancels the gravitational force. What is the distance between the two?

Homework Equations


F=Eq
F=ma
F=kq1q2/r^2

The Attempt at a Solution


I honestly don't know at all how to solve this. If someone could explain to me how and maybe show me the initial steps, that would be great!
 
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We aren't supposed to help before you make an attempt.
But I can give you a little hint. Just write the obvious:
force of gravity = electric force
Then look for the formula for each side of the equation and write the next step in formulas. Solve for the quantity you want to find. Put in the numbers and run it through your calculator.
 

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