Minimal Launch Velocity needed

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The discussion revolves around determining the minimal launch velocity required for a negatively charged particle to escape from a positively charged dielectric sphere. Key considerations include calculating the potential energy of the particle at the sphere's surface and at infinity, as well as the forces acting on it. The concept of escape velocity is referenced to draw parallels with gravitational fields. Additionally, the impact of increasing the sphere's radius on the required launch velocity is questioned. Understanding these factors is essential for solving the problem effectively.
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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!
 
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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?
 
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)?
 

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