Question

Two conducting spheres, one of radius 0.020 m. and the other of radius 0.170 m., each have a charge 7.00E-08 C. and are very far apart. If the spheres are connected by a conducting wire, find the final potential (in volts) in each sphere.

Answer 1

for sphere with radius r1 = 0.02 m

potential V1 = k*Q/r1

for sphere with radius r2 = 0.17 m

potential V2 = k*Q/r2

V1 > V2

the charge flows from sphere 1 to sphere 2

untill the both are at same potential

let q charge flows from sphere 1 to sphere 2

v1' = v2'

K*(Q-q)/r1 = k*(Q+q)/r2

(Q-q)/r1 = (Q+q)/r2

(7*10^-8 - q)/0.02 = (7*10^-8 + q)/0.17

q = 5.526*10^-8 C

potential V1' = 9*10^9*(7*10^-8-5.526*10^-8)/0.02 = 6633 V

potential V2' = 9*10^9*(7*10^-8+5.526*10^-8)/0.17 = 6633 V