Minimal Launch Velocity needed

[UTGirl24]

Homework Statement

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 p). What minimal “Launch velocity” v0 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?

Homework Equations

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The Attempt at a Solution

Please help!

 

[olivermsun]

Hints:

What is the potential energy of the particle currently (at distance R)?

What will the potential energy of the particle be if it really does manage to fly off to infinity?

 

[CompuChip]

Suppose that the particle is at a distance $r \ge R$ from the center of the sphere.
What is the force exerted on it?

Also, have you ever seen the concept of 'escape velocity' (e.g. for rockets in a gravitational field)?