A spherical shell of radius `R` has two holes `A` and `B` through which a ring having charge `+q` passes through without touching the shell. The flux through spherical shell is `(q)/(3epsilon_(0))`. Find the radius of the ring.

Options

A. `Rsqrt(2)`
B. `2R`
C. `0.5R`
D. `R`

Answer

D

Explanation

Charge responsible for producing flux in the shell `=q//3`. In this case, angle formed by the shell at centre of ring `(q)/(3 epsilon_(0))`
So, charge to contribute flux in the shell
`=(2pi)/(3)(q)/(2pi)= (q)/(3)`
It is possible only if radii of ring and shell are equal and circumference of each passes through the centre of the other.
So, radius of ring `R`