Two protons are aimed directly toward each other by a cyclotron accelerator with

Question

Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 2.00×105 m/s , measured relative to the earth. Part A Find the maximum electrical force that these protons will exert on each other. A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge q on the outer spherical shell. Take V to be zero when r is infinite. Part E Use the equation Er=Vr and the result from part (b) to find the electric field at any point between the spheres (ra

Explanation / Answer

The initial kinetic energy of the two protons will equal the electrostatic potential energy at closest approach.
2(0.5)(1.67 x 10^-27)(2.00 x 10^5)^2 = kq^2/d = (9 x 10^9)(1.602 x 10^-19)^2/d
d = 3.4577 x 10^-12 m
F = kq^2/d^2 = (9 x 10^9)(1.602 x 10^-19)^2/(3.4577 x 10^-12)^2 = 1.932 x 10^-5 N

the potential outside the sphere is zero i.e for r" > r'
Note that if were not defined in the introduction, the exact value for the potential could not be calculated (since potential is always in terms of some reference potential), only the potential difference . Moreover, the value for that you calculate for the region is valid only for the region outside of both spheres, as you will see in the following parts.


for r < r" < r' , the potential is
= -k*q(r"-r)/rr"
and for r" < r
potential is -kq*(r-r')/rr'

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