To solve this problem we will apply the principles of energy conservation. The kinetic energy in the object must be maintained and transformed into the potential electrostatic energy. Therefore mathematically
[tex]KE = PE[/tex]
[tex]\frac{1}{2} mv^2 = \frac{kq_1q_2}{r}[/tex]
Here,
m = mass (At this case of the proton)
v = Velocity
k = Coulomb's constant
[tex]q_{1,2}[/tex] = Charge of each object
r= Distance between them
Rearranging to find the second charge we have that
[tex]q_2 = \frac{\frac{1}{2} mv^2 r}{kq_1}[/tex]
Replacing,
[tex]q_2 = \frac{\frac{1}{2}(1.67*10^{-27})(3*10^5)^2(7*10^{-2})}{(9*10^9)(1.6*10^{-19})}[/tex]
[tex]q_2 = 3.6531nC[/tex]
Therefore the charge on the sphere is 3.6531nC
