Electrostatic Force Exerted Between Two Protons

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Homework Help Overview

The discussion revolves around the electrostatic force exerted between two protons and how to balance this force with the gravitational force acting on one of the protons near the Earth's surface. The problem involves applying Coulomb's law and gravitational force concepts.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the application of Coulomb's law to determine the distance required for the electrostatic force to equal the gravitational force on a proton. There are attempts to solve for the distance using equations, and questions arise regarding the correctness of initial calculations and assumptions about the forces involved.

Discussion Status

Some participants have shared their attempts at solving the problem, with one noting a specific calculation that was initially incorrect. Another participant later reports a successful calculation, indicating a potential resolution to the problem. However, there is no explicit consensus on the methods used or the reasoning behind the initial errors.

Contextual Notes

Participants discuss the need to equate the gravitational force (weight) with the electrostatic force, emphasizing the importance of correctly applying the relevant formulas. There is mention of gravitational force acting on the proton and the necessity of understanding both forces to solve the problem.

tjrana0
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A proton is in a vacuum near the surface of Earth. Where should a second proton be placed so that the electrostatic force it exerts on the first proton balances the weight of the first proton?

F = (k×Abs[q1]×Abs[q2]) / r^2
k = 8.99×10^9 Nm^2/C^2
 
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You need to post your attempt.
 
The first attempt, I got 1.51911E-14 which was incorrect.
It says "Did you use the Coulomb equation to get the electrostatic force? Do you recall how to calculate the gravitational force on an object (the weight) near Earth's surface?"
I did do all of the above, but with no success.

proton = 1.602176 10^-19;

Solve[1 == (k proton^2)/r^2, r]
{{r -> -1.51911*10^-14}, {r -> 1.51911*10^-14}}
This was the answer that was incorrect.
I thought that the left side of the equation was 1, for some reason, I'm not sure. If it is 0, then the equation is unsolvable. What did I do wrong?
 
tjrana0 said:
The first attempt, I got 1.51911E-14 which was incorrect.
It says "Did you use the Coulomb equation to get the electrostatic force? Do you recall how to calculate the gravitational force on an object (the weight) near Earth's surface?"
I did do all of the above, but with no success.

proton = 1.602176 10^-19;

Solve[1 == (k proton^2)/r^2, r]
{{r -> -1.51911*10^-14}, {r -> 1.51911*10^-14}}
This was the answer that was incorrect.
I thought that the left side of the equation was 1, for some reason, I'm not sure. If it is 0, then the equation is unsolvable. What did I do wrong?

If it is near the surface of the Earth, then a gravitational force acts on it, its weight, mg.

You want the weight to be the same the electric force.

So you need to equate mg to the formula for the electrostatic force.
 
I did 1.6762622*10^-27*9.80665 == 8.99*10^9*1.602*10^-19*1.602*10^-19/r^2
and solved for r and got the right answer! Thank you!

Solve[1.6762622*10^-27*9.80665 ==
8.99*10^9*1.602*10^-19*1.602*10^-19/r^2, r]
{{r -> -0.118471}, {r -> 0.118471}}

r=0.118471m
 
Last edited:

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