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Query created by MadelineChef: how would the minimal launch velocity change?
A small negatively charged particle (mass m, charge -q) is currently at rest at the surface of a large positively and uniformly charged dielectric sphere (radius R, charge density rho). What minimal “launch velocity” v_o should be given to this particle so that it could leave the attracting “mother” sphere to travel to infinitely remote places? If the radius R of the sphere is increased by a factor of 2 (everything else left the same), how would the minimal launch velocity change?
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Solution:
Answer by rs
This is the same as escape velocity.
Here is a hint.
Figure out the potential energy at the surface.
At the time the particle escapes, it has zero potential energy due to the charged sphere. I never really has exactly zero, but for all practical purposes, you can assume zero.
Figure out the kinetic energy needed to match the difference in potential energy from the surface to zero.
Be sure much better?
Leave the answer as part of his comments!
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