A point charge `+Q` is placed at a distance r from a short dipole of dipole moment `vecp` as shown in figure. The line joining the point charge Q to the centre dipole is perpendicular to dipole moment `vecp`, which of the following statement are true?

Options

A. The net electrostatics force on the dipole is zero
B. The electrostatics force on the dipole in `(Qp)/(4piepsilon_(0)r^(3))` and is acting along the dipole moment `vecp`.
C. Torque acting on dipole is `(Qp)/(4piepsilon_(0)r^(2))` in inward direction.
D. torque acting on the dipole is `(Qp)/(2piepsilon_(0)r^(2))` in inward direction.

Answer

B, C

Explanation

`F_("net")=2Fsintheta`
`=(Kqa)/((a^(2)+r^(2)))(a)/(sqrt(a^(2)+r^(2)))=(KQp)/((a^(2)+r^(3))^((3)/(2)))`
`=(Qp)/(4piepsi_(0)r^(3))`
`tau_(net)=2Fcosthetaxxa=(Qp)/(4piepsi_(0)r^(2))`