Two short dipoles `phat(k)` and `P/2 hat(k)` are located at `(0,0,0)` & `(1m, 0,2m)` respectivley. The resultant electric field due to the two dipoles at the point `(1m, 0,0)` is

Options

A. `(9p)/(32piepsilon_(0)hat(k)`
B. `(-7p)/(32piepsilon_(0)hat(k)`
C. `(7p)/(32piepsilon_(0)hat(k)`
D. None of these

Answer

B

Explanation

The given point is at axis of `(vec(p))/(2)` dipole and at equatorial line of `vec(p)` dipole so total field at given point is
`vec(E)=-(kvec(p))/((1)^(3))+(2k(vec(p)//2))/((2)^(3))=kvec(p)(-1+(1)/(8))=(-7vec(p))/(32piepsilon_(0))`