Two charges of $-4 \ \mu C$ and $+4 \ \mu C$ are placed at the points $A(1, 0, 4) \ m$ and $B(2, -1, 5) \ m$ located in an electric field $\vec{E} = 0.20 \ \hat{i} \ V/cm$. The magnitude of the torque acting on the dipole is $8 \sqrt{\alpha} \times 10^{-5} \ Nm$. Where $\alpha = $ . . . . . .

An electric dipole is kept on the axis of a uniformly charged ring at a distance of $R/\sqrt{2}$ from the center of the ring. The direction of the dipole moment is along the axis. The dipole moment is $P$,the charge of the ring is $Q$,and the radius of the ring is $R$. The force on the dipole is nearly:

Electrical field intensity due to an electric dipole on its axis at distance $x$ $(x \gg a)$ and on the equatorial line at distance $y$ $(y \gg a)$ are same. What is the ratio of $x$ and $y$?

Write the expression for the torque experienced by an electric dipole placed in a uniform electric field.

$A$ positive charge $Q$ is distributed uniformly over a circular ring of radius $R$. $A$ point particle having a mass $m$ and a negative charge $-q$ is placed on its axis at a distance $x$ from the centre. Assuming $x \ll R$,find the time period of oscillation of the particle,if it is released from there [neglect gravity].

Three point charges $+q$,$-2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0)$,$(x = 0, y = 0, z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are