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 × 10-3C

Question

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 × 10-3C (A) 40 (B) 30 (C) 20 (D) 10

Tardigrade Admin · Accepted Answer

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.

∴ V_{1} = V_{2}

\frac{q _{1}}{4 π ε _{0} r _{1}} = \frac{q _{2}}{4 π ε _{0} r _{2}}

\Rightarrow \frac{r _{1}}{r _{2}} = \frac{q _{1}}{q _{2}} = \frac{15 m C}{45 m C} = \frac{1}{3}

Final charge on first sphere,

q_{1} = \frac{1}{3} (q_{1} + q_{2}) = \frac{1}{3} \times 60 = 20 m C

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

40

30

20

10

Q. Two metal spheres of radii $0.01 m$ and $0.02 m$ are given a charge of $15 m C$ and $45 m C$ respectively. They are then connected by a wire. The final charge on the first sphere is _____ $\times 1 0^{- 3} C$