Three identical dipoles are arranged as shown below. What will be the net electric field at `P`? `(k=1/(4pi epsilon_(0)))`

Options

A. `(k.p)/(x^(3))`
B. `(2kp)/(x^(3))`
C. Zero
D. `(sqrt(2)kp)/(x^(3))`

Answer

C

Explanation

Point `P` lies at equatorial positions of dipole `1` and `2` and axial positions of dipole `3`.
Hence field at `P` due to dipole `1`,
`E_(1)= (k.p)/(x^(3))`(toward left)
due to dipole 2,
`E_(2)=(k.p)/(x^(2))` (toward left)
due to dipole 3,
`E_(3)=(k(2p))/(x^(3))`(toward right)
So net field at `P` will be zero.