Two concentric rings, one of radius `R` and total charge `+Q` and second of radius `2R` and total charge `-sqrt(8)Q`, lie in `x-y` plane (i.e., `z=0`plane). The common centre of rings lies at origin and the common axis coincides with `z`-axis. The charge is uniformly distributed on both rings.
At what distance from origin is the net electric field on `z`-axis zero?

Options

A. `(R )/(2)`
B. `(R )/(sqrt(2))`
C. `(R )/(2sqrt(2))`
D. `sqrt(2)R`

Answer

D

Explanation

Electric field at a point on `z`-axis distant `r` from origin is
`E=1/(4piepsilon_(0))((Qr)/((r^(2)+R^(2))^(3//2))-(sqrt(8)Qr)/((r^(2)+4R^(2))^(3//2)))=0`
Solving we get `r= sqrt(2)R`