The electric field $\vec{E}$ at a point at a distance $r$ from the axis of a dipole is given by:

An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole is zero when $\theta = 90^o$,the torque and the potential energy of the dipole will respectively be

Two parallel disks each having radius $R$ are separated by a distance $l$. The surface charge densities are $\sigma$ and $-\sigma$. The electric field at point $P$,a large distance $r$ along the axis of the disks is:

Consider a positively charged infinite cylinder with uniform volume charge density. An electric dipole consisting of $+Q$ and $-Q$ charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,

An electric dipole is placed at the origin in the direction of the $x$-axis. $A$ point $P$ is at a distance of $20 \, cm$ from the origin $O$ such that $OP$ makes an angle of $\pi/3$ with the $x$-axis. If the electric field at point $P$ makes an angle $\theta$ with the $x$-axis,then the value of $\theta$ 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