Two conducting sphere of radii 6 cm 12 cm each having the same charge 3 × 10-8C, are kept very far apart. If the sphere are connected to each other by a conducting wire, find. . .

Problem : Two conducting sphere of radii 6 cm 12 cm each having the same charge 3 × 10^-8C, are kept very far apart. If the sphere are connected to each other by a conducting wire, find
a) the direction and amount of charged transferred and
b) find potential of each sphere.

Doubt by Meghna

Solution :

We know.

V = kq/r
V∝ 1/r

The sphere of smaller radius has large potential then the sphere of large radius. Hence charges will flow from small sphere of 6 cm radius to large sphere of 12 cm radius. .
These charges will keep on flowing until the potential becomes equal.

q₁ = C₁V

q₂ = C₂V

We know,

q ∝ C ∝ r

q = q₁ + q₂ = 2q₁ = 2q₂

r₁ = r

r₂ = 2r

q1' = [r₁/(r₁+r₂)]q = [q/3] = 2q₁/3

q2' = [r₂/(r₁+r₂)]q = [2q/3] = 4q₁/3

Total Change Transferred
=  q₁-2q₁/3 = q₁/3 = 10^-8 C

Common Potential (V_C) = [(C₁V₁+C₂V₂)]/(C₁+C₂)

= (q₁+q₂)k/r₁+r₂

= 2qk/3r

= (6 × 10^-8 × 9 × 10⁹)/3×6 ×10^-2

= 3 × 10³ V

= 3000 V