Question

A soap bubble of radius $R$ with wall thickness $t$ is charged to a potential $V_0$. The bubble bursts and becomesa spherical drop of soap solution of radius $r$. Now, it has potential, $V$. Assume, the soap solution to be a conductor.

Then the charge carried by the soap bubble is :

• A. $4\pi {\epsilon }_{0}R{V}_0$
• B. $2\pi {\epsilon }_{0}R{V}_0$
• C. $4\pi {\epsilon }_{0}rV$
• D. Both (A) and (C)

Answer 1

Answer: (D)

Both (A) and (C)

For the bubble case,
$V_0=kQ/R\Rightarrow Q=4\pi {ϵ}_0{V}_{0}R$
For the drop case,
$V=kQ/r\Rightarrow Q=4\pi {ϵ}_{0}Vr$