A conducting bolloon of the radius a is charged to potential `V_(0)` and held at a large height above the earth ensures that charge distribution on the surface of the balloon remains unaffected by the presence of the earth. It is connected to the earth through a resistance R and a value in the balloon is opened . The gas inside the balloon escapes from value and the size of the balloon decreases. The rate of decrease in radius of the balloon is controlled in such a manner that potential of the balloon remains constant. Assume the electric permittivity of the surrounding air equals to that of free space `(epsilon_(0))` and charge cannot leak to the surrounding air.

The rate at which radius r of the balloon changes with time is best represented by the equation

Options

A. `(dr)/(dt)=(1)/(4piepsilon_(0)R)`
B. `(dr)/(dt)=-(1)/(4pi epsilon_(0)R)`
C. `(dr)/(dt)=(1)/(4pi epsilon_(0)aR)`
D. `(dr)/(dt)=-(r)/(4pi epsilon_(0)aR)`

Answer

B