Question

A pith ball, which has a residual charge of 66.0 micro C is brought into contact with a second pith ball, which has an initial residual charge of -33.0 micro C and which has twice the surface area of the first pith ball. What will be the final residual charge on each pith ball after they have been separated?

Answer 1

total initial charge = 66 - 33

= 33 mciro C

let q1 and q2 are the charges on each ball after separating.

q1 + q2 = 33*10^-6 --------(1)

let r1 = r

let r2 is the radius of the second pith ball.

A2 = 2*A1

pi*r2^2 = 2*pi*r1^2

r2 = sqrt(2)*r

when they separate, V1 = V2

k*q1/r1 = k*q2/r2

q1/r = q2/(sqrt(2)*r)

q1*sqrt(2) = q2

q1 + q2 = 33 micro C

q1 + sqrt(2)*q = 33 micro C

q1*(1 + sqrt(2)) = 33

q1 = 33/(1 + sqrt(2))

= 13.6 micro C (charge on small ball) <<<<<<<-----Answer

q2 = sqrt(2)*13.7

= 19.4 micro C (charge on larger ball) <<<<<<<-----Answer