What Speed Must an Electron Achieve to Orbit a Charged Sphere?

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SUMMARY

The problem involves calculating the speed required for an electron to orbit a charged glass sphere with a diameter of 2.40 mm and a charge of +1.70 nC, at a distance of 1.40 mm above its surface. The relevant equations include the electric field of the sphere, given by E = k * Q / (r^2), and the centripetal force equation q * E = M * v^2 / r. The correct radius for calculations must include both the radius of the sphere and the additional distance from its surface to the electron's orbit.

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  • Familiarity with centripetal force and motion equations
  • Knowledge of basic physics concepts related to charged particles
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  • Study the concept of electric fields around charged objects, specifically using the formula E = k * Q / (r^2)
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  • Practice similar problems involving charged spheres and orbiting particles to reinforce understanding
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dtesselstrom
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Homework Statement


A 2.40 -mm-diameter glass sphere has a charge of + 1.70 nC.
What speed does an electron need to orbit the sphere 1.40 mm above the surface?

Homework Equations


Electric Field of Sphere: E=k*Q/(r^2)
q*E=M*v^2/r


The Attempt at a Solution


It seems pretty straight forward but I must be doing something wrong with the r values. Could someone tell me what the radius is considered. For the electric field is it the radius of sphere + the distance away or what and same for the other equation. I've tried pretty much all the combos I can think of and still am getting it wrong so not sure where I am going wrong.
 
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It says above the surface so you would have to add the radius of the sphere to the radius of the orbit.
 
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