Two charged metallic spheres with radii \( R_1 \) and \( R_2 \) are brought in contact and then separated. The ratio of final charges \( Q_1 \) and \( Q_2 \) on the two spheres respectively will be ____________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{Q_1}{Q_2} = \frac{R_1}{R_2} \)
When two conductors touch, charge flows between them until they reach the same potential. The potential of an isolated sphere of radius \( R \) carrying charge \( Q \) is \( V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R} \).
\( \displaystyle \frac{1}{4\pi\varepsilon_0}\,\frac{Q_1}{R_1} = \frac{1}{4\pi\varepsilon_0}\,\frac{Q_2}{R_2} \)
\( \displaystyle \frac{Q_1}{Q_2} = \frac{R_1}{R_2} \)
So the charge is shared in proportion to the radii: the larger sphere keeps the larger share.