The centers of two metal spheres of radius 10 cm are 60 cm apart on the x-axis.

Question

The centers of two metal spheres of radius 10 cm are 60 cm apart on the x-axis. The spheres are initially neutral, but a charge Q is transferred from one sphere to the other, creating a potential difference between the spheres of 210 V. A proton is released from rest at the surface of the positively charged sphere and travels to the negatively charged sphere. At what speed does it strike the negatively charged sphere? The fundamental charge is 1.602 times 10 - 19 C and the mass of a proton is 1.6726 times 10-27 kg. Answer in units of m/s

Explanation / Answer

since electrostatic fields are conservative fields, problem can be solved by conserving energy of proton.

change in potential energy of proton = q*(difference in potential between spheres)=1.602e-19*210=336.42e-19 J

this energy must be converted into kinetic energy

change in KE=.5*m*v^2-0 (since it starts from rest)

=> change in KE=change in PE

=> v^2=2*336e-19/(1.6726e-27)=402.271911993e8

=>v=200567.1737 m/s

=> velocity of proton at the surface of negatively charged sphere is 2.00567 X10^5 m/s

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