The magnitude of electric field intensity at point `B (2 , 0, 0)` due to a dipole of dipole moment `vec(P) = hati + sqrt(3)hatj` kept at origin is (assum that the point B is at a large distance from the dipole end `K = 1/(4 pi epsilon_0)`)

Options

A. `(sqrt(13)K)/8`
B. `(sqrt(13) k)/4`
C. `(sqrt(7)k)/8`
D. `(sqrt(7)k)/4`

Answer

C

Explanation

The dipole moment makes an angle `60^(@)` with x-axis and lies in x-y plane as shown in figure

The electric field at point A due to dipole's
`E=(kP)/(r^(3)) sqrt(1+3 cos^(2)theta)` where `theta=60^(@)` `:. E=(sqrt(7)K)/8`
Alternate solution
The dipole of moment P can be taken as combination of two dipole moments `vec(P)_(1)=hati` and `vec(P)_(2)=sqrt(3)hatj` as shown in figure

the electric field at point A is
`vec(E)=k(2vec(P)_(1))/(r^(3))-k(vec(P)_(2))/(r^(3))=k[(2hati)/(2^(3))-(sqrt(3)hatj)/(2^(3))]rArr |vec(E)|=(sqrt(7)K)/8`