# Radially oscillating charged soap bubble

**Electricity and Magnetism**Level 5

A **neutral** soap bubble has a radius \(R\), mass \(M\), and the liquid making its boundary has surface tension \(\sigma\). Now, this soap bubble is given a very small charge \(q\). Afterwards , it begins oscillating radially(i.e. its radius oscillates with a particular frequency).The time period of these oscillations can be shown as \(T_{0} = \sqrt{\dfrac{a \pi M}{b P_{A} R + c \sigma}}\), where \(P_{A}\) is atmospheric pressure, and \(a,b,c\) are co-prime integers . Find the value of \(a+b+c\).

**Details and assumptions**

\(\bullet\) The gas inside the bubble is ideal and mono-atomic.

\(\bullet\) No heat exchange takes place, i.e. the boundary is insulating.

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