A point charge `+q` is moved with a constant velocity v toward a solid conducting sphere carrying a charge Q. Find the (a) potential of the sphere, (b) charge induced as the function of r, (c ) charge flowing if we close the key K, and (d) current is the part (c ).

Explanation

a. We find potential at the center of sphere.
`V =(kq)/(r ) +(kQ)/(R ) = (1)/(4piepsilon_0)[(q)/(r ) +(Q)/(R )]`
b. If key is closed, potential of sphere should be zero.
`V = 0 or k((q)/(r ) +(Q)/(R )) = 0 or Q = -(qR)/(r )`
c. Charge flowing through key is `q' = (qR)/(r )`
d. `I = (dq)/(dt) = (dR)/(-r^2) (dr)/(dt) = (dR)/(-r^(2))(-v) = (qRv)/(r^(2))`