Two coaxial rings, eacg of radius R, made of thin wire are separated by a small distabce `l(l lt lt R)` and carry the charges `q` and `-q`. Find the electric field potential and strength at the axis of the system as a function of the x coordinate (see figure). Investigate these functions at `|x| gt gt R`

Answer

`V=(ql)/(4 pi epsilon_(0))(X)/((R^(2)+X^(2))^(3//2))`
`E = -(ql)/(4 pi epsilon_(0))((R^(2)-2X^(2)))/((R^(2)+X^(2))^(5//2))`

Explanation

`V = (kq)/(sqrt(R^(2)+(x-(l)/(2))^(2)))-(kq)/(sqrt(R^(2)+(x+(l)/(2))^(2)))`
`because x gt gtR` Dipole
`V = (kp)/(r^(2))=(kql)/(x^(2)) rArr E =(2kp)/(r^(2))=(2kql)/(x^(3))`.