Question

There are two spheres having same charge q and radii R and 2R. What will be the charge on each
sphere if both are connected and then separated ?

Answer 1

Let the initial charges on spheres with radius R = q

Let the initial charges on spheres with radius R2 = q2

Since, the charge surface charge density of both the spheres is same  -

= q1/4πr² = q2/4π(2r)²

= 4q1 =q2

Total charge = 5q2

Let the charges now on each sphere be Q1 and Q2 respectively

=> kQ1/R = kQ2/2R

=> 2Q1 =Q2

Total charge = Q1+ Q2 = 3Q2

 Since, the total charge is conserved

= 5q1 =3Q2 = 3(2Q1) =6Q1

= Q1 = 5q1/6

Final charge density

= kQ1/R

= 5kq1/6R