What Is the Escape Speed of an Electron from a Charged Glass Sphere?

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SUMMARY

The escape speed of an electron from a charged glass sphere with a diameter of 1.0 cm and a charge of 10 nC is calculated using the formula for potential energy and kinetic energy. The initial calculation mistakenly used a radius of 0.05 cm instead of the correct radius of 0.5 cm (0.005 m). After correcting the radius, the accurate escape speed is determined to be 8.0 x 107 m/s, resolving the initial error of 2.5 x 108 m/s.

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  • Understanding of electrostatics, specifically Coulomb's law
  • Familiarity with kinetic and potential energy equations
  • Basic knowledge of unit conversions, particularly between centimeters and meters
  • Proficiency in algebra for solving equations
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  • Study Coulomb's law in detail to understand electrostatic forces
  • Learn about energy conservation principles in physics
  • Explore the concept of escape velocity in different contexts, such as planetary bodies
  • Practice solving problems involving charged particles and electric fields
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Students in physics, particularly those studying electrostatics and energy conservation, as well as educators looking for examples of problem-solving in electrostatic scenarios.

mitchy16
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Homework Statement


What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10nC?

Homework Equations


Given:
d= 1.0cm
r= 0.05cm= 0.0005m
q1 = 10nC = 10 x 10-9 (sphere)
q2 = -1.6 x 10-19 (electron)

Equation:
U = (kq1q2)/r
KE= ½mv2

The Attempt at a Solution


So, if the sum of kinetic and potential energy is supposed to be zero, then I get:

KE + U = 0
½me(ve)2 + (kq1q2)/r = 0
½(9.11 x 10-31)(v)2 + ( (8.99 x 109) (10 x 10-9) (-1.6 x 10-19) ) / (0.0005) = 0

If I solve the above equation^^, I get ve= 2.5 x 108 m/s, which is incorrect. The correct answer is 8.0 x 107 m/s. I am not sure what I am doing incorrectly, any help is appreciated. Sorry about the mess, I can't seem to figure out how to use TeX!
 
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Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!
 
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Delta² said:
Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!
Thank you, can't believe I didn't catch that. I re-did and got the correct answer!
 

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