Two metal spheres of radii 0.01 ~m and 0.02 ~m are given a charge of 15 mC and 45 mC respectively. They are then connected by a wire. The final charge on the first sphere is . 10⁻³ C .

Step-by-step solution

When two metal spheres are joined by a wire, charge flows from one at higher potential to the other at lower potential, till they acquire the same potential. aligned V₁ &=V₂ q₁ 4 ₀ r₁ &= q₂ 4 ₀ r₂ aligned r₁ r₂ = q₁ q₂ = 15 m C 45 m C = 1 3 Final charge on first sphere, q₁= 1 3 (q₁+q₂ )= 1 3 60=20 mC