Two metal spheres of same radius R are placed at a very large distance from each other, and they are connected by a coil of inductance L, as it is shown in the figure. One of the spheres is loaded with electric charge. At what time, after closing the switch S. does the charge on this sphere decreases to half ?

Options

A. `(pi)/(2)sqrt(4piepsilon_(0)LR)`
B. `(pi)/(4)sqrt(4piepsilon_(0)LR)`
C. `(pi)/(2)sqrt(2piepsilon_(0)LR)`
D. `(pi)/(4)sqrt(2piepsilon_(0)LR)`

Answer

C

Explanation

`C = 2pi epsilon_(0)R`
`T = 2pi sqrtLC = 2pi sqrt(2pi epsilon_(0)RL)`
Required times `= (T)/(4) = (pi)/(2) sqrt(2pi epsilonLR)`