A short electric dipole is oriented along x-direction at origin. At which of following point the electric field have no x component.

Options

A. `(1,1,0)`
B. `(sqrt(2),1,0)`
C. `(1,sqrt(2),0)`
D. `(1,0,0)`

Answer

C

Explanation

`E_(r)=(2kpcostheta)/r^(3)`
`E_(0) = (kp sintheta)/r^(3)`
`E_(x)=E_(1)cos theta -E_(theta) sintheta = (kp)/r^(3)[2cos^(2) theta-sin^(2)theta]`
`E_(x) = (kp)/r^(3)[2-3sin^(2) theta]`
For the point `=(1,sqrt(2),0), sin theta = sqrt(2)/sqrt(3) hence E_(x)=0`