If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$,then the torque acting on it is given by:

Three charges are arranged on the vertices of a right-angled triangle as shown in the figure. The magnitude of the dipole moment of the combination in the unit of $C-cm$ is:

Two electric dipoles of dipole moments $1.2 \times 10^{-30} \, C \cdot m$ and $2.4 \times 10^{-30} \, C \cdot m$ are placed in two different uniform electric fields of strengths $5 \times 10^{4} \, N \cdot C^{-1}$ and $15 \times 10^{4} \, N \cdot C^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is $.....$

Three point charges $q, -2q$ and $q$ are placed along the $x$-axis at $x = -a, 0$ and $a$ respectively. As $a \rightarrow 0$ and $q \rightarrow \infty$ while $qa^2 = Q$ remains finite, the electric field at a point $P$, at a distance $x$ $(x \gg a)$ from $x = 0$ is $E = \frac{\alpha Q}{4 \pi \epsilon_0 x^\beta} \hat{i}$. Then:

Point charges are fixed at the hour marks of a wall clock as shown. If the net dipole moment of the system is along the direction of the hour hand,then the time shown by the clock is:

The electric field at a point due to an electric dipole,on an axis inclined at an angle $\theta$ $(< 90^{\circ})$ to the dipole axis,is perpendicular to the dipole axis,if the angle $\theta$ is