A metal target sphere of 20 cm diameter suspended out in space is given a charge

Question

A metal target sphere of 20 cm diameter suspended out in space is given a charge of +1.00 nC. How much work must be done on a proton in taking it from very far away (essentially infinity) to the surface of the sphere?
With the previous probelm in mind, through what voltage must the proton be accelerated from rest (by some sort of space weapon) if it is to arrive at the sphere at a speed of 8.5 x 10^4 m/s? Neglect any gravitational effects.


Please tell me how to solve it and answers. (Explain please!)

Explanation / Answer

diameter d = 20 cm radius r = d/ 2 = 10 cm = 0.1 m charge q = 1 * 10 ^ -9 C Potential on the surafce of the sphere V = Kq / r where K = coulomb's constant = 8.99 * 10 ^ 9 Nm^ 2/ C^ 2 plug the values we get V = 89.9 volts Therefore work must be done on a proton in taking it from very far away to the surface of the sphere W = Ve where e = charge of proton = 1.6 * 10 ^ -19 C plug the values we get W = 1.43 * 10 ^ -17 J (b). Initial speed u = 0 final speed v = 8.5 x 10^4 m/s we know ,V' q = ( 1/ 2) m[ v^ 2- u^ 2] = ( 1/ 2) mv^ 2 required voltage V ' = (1/2q) mv^ 2 where m = mass = 1.67 * 10 ^ -27 kg = 37.7 volt q = charge = 1.6 * 10 ^ -19 C

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