Electrostatic and gravitational forces

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SUMMARY

The discussion centers on calculating the distance required for a proton to be positioned from a group of 13 protons such that the electrostatic force equals the gravitational force acting on a proton at Earth's surface. The relevant formulas include Coulomb's Law, represented as \( F = \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r^2} \), and the gravitational force \( F = mg \). The user calculated a distance of approximately 43.7 cm, but expressed confusion regarding the inclusion of the 13 protons in the calculation. The correct approach involves recognizing that the electrostatic force from multiple protons must be summed appropriately.

PREREQUISITES
  • Understanding of Coulomb's Law and electrostatic forces
  • Basic knowledge of gravitational force calculations
  • Familiarity with the constants: mass of a proton (1.67 x 10^-27 kg) and charge of a proton (1.6 x 10^-19 C)
  • Ability to manipulate algebraic equations involving physical constants
NEXT STEPS
  • Review the principles of Coulomb's Law and its application in multi-charge systems
  • Study gravitational force calculations and their comparison to electrostatic forces
  • Explore the concept of electric field strength and its relation to distance
  • Investigate the implications of force balance in electrostatics and gravitation
USEFUL FOR

Students in physics, educators teaching electrostatics and gravitation, and anyone interested in understanding the forces acting on charged particles.

Rowie25
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Homework Statement


How far (in cm) apart must be proton from group of 13 protons if the magnitude of the electrostatic force acting on either one due to the others is equal to the magnitude of the gravitational force on a proton at Earth's surface?


So, I know that the mass of a proton is 1.67*10^-27 kg and that the charge on the proton is 1.6*10^-19 C. I am using the formula: 1/(4piEo) times (q1q2 divided by r^2) equals mg. So I thought you could set it up like this: (1.6*10^-19 times (13)(1.6*10^-19) divided by (1.6*10^-27)(9.8). That multiply that quotient by r^2=9*10^9. I don't think I did it right, I'm confused at what to do with the 13. Thanks!
 
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I got something like .437 meters and changed that into 43.7 centimeters. Does that seem right?
 

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