Two conducting spheres of radii 5 cm and 10 cm are given a charge of \( 15\,\mu\mathrm{C} \) each. If the two spheres are now joined by a conducting wire, the charge on the smaller sphere will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 10\,\mu\mathrm{C} \)
When two conductors are joined by a wire, charge flows until they reach the same potential. The total charge is conserved.
\( \displaystyle \frac{q_1}{4\pi\varepsilon_0\,r_1} = \frac{q_2}{4\pi\varepsilon_0\,r_2} \;\Rightarrow\; \frac{q_1}{q_2} = \frac{r_1}{r_2} = \frac{5}{10} = \frac{1}{2} \)
So the charge divides in the ratio of the radii. Total charge:
\( q_1 + q_2 = 15 + 15 = 30\,\mu\mathrm{C} \)
\( \displaystyle q_1 = 30 \times \frac{1}{1 + 2} = 10\,\mu\mathrm{C} \)
The larger sphere keeps \( 20\,\mu\mathrm{C} \).