Two electric dipoles, A, B with respective dipole moments `d_(A)=-4qahati` and `d_(B)=-2qahati` are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is:

Options

A. `R/(sqrt2-1)`
B. `R/(sqrt2+1)`
C. `(sqrt2R)/(sqrt2-1)`
D. `(sqrt2R)/(sqrt2+1)`

Answer

C

Explanation

Potential should be of sign
`4/((R+x)^(2))=2/((x)^(2))`
`rArr2x=sqrt2R+sqrt2xrArrx=(sqrt2R)/(2-sqrt2)=R/(sqrt2-1)`
Ans is x + R `=(sqrt2R)/(sqrt2-1)`