How Fast Does a Charged Particle Move Away from a Similarly Charged Sphere?

[juicev85]

okay there are several problems in my physics book that really have me stumped. I just want to learn a method of solving them. basically they have to do with a sphere of a given diameter and charge. The problem then says assume a subatomic particle (electron or proton) is placed on the sphere and the sphere is charged to the same charge(ie if the particle was a proton the charge on the sphere would be positive). The charge on the sphere is much higher than on the particle. then it asks how fast is the particle moving away from the sphere at a given distance away.

I would really appreciate any hints or formulas that I could use to solve these types of problems.

 

[Hootenanny]

You will probably need coulomb's law:
$$F = \frac{q_1 \cdot q_2}{4\pi \epsilon_0 r^2}$$
Try http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c1 for more info.

 

[DaMastaofFisix]

Ookay, probably need columbs law and some feedback from conservation of energy and such. What they are trying to get at is that for any geometrical figure (no matter the orientation and shape) the electric field produced by the net charge outside of its radius can be thought of as a point charge concentrated on its center of mass (in this case, the center of the sphere). This is actually an extension of Gausses law, a simple calculus related method to finding electric fields and such. In any event, once that has been established, and the charges and radius (or half the diameter is known), its all a matter of the forces acting on each chraged particle (or sphere). That's where columbs law comes into play. From that, the acceleration of the proton can be calculated at any given distance. Take this as a starting point.