B M Sharma Solutions for Chapter: Coulomb's Laws and Electric Field, Exercise 6: DPP

Three charges of $\left(+2q\right),\left(-q\right) \text{and} \left(-q\right)$ are placed at the corners $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of an equilateral triangle of side $a$ as shown in the adjoining figure. Then the dipole moment of this combination is 

Three identical small dipoles are arranged as shown in the figure. What will be the net electric field at $P$? ($k=\frac{1}{4\pi {\epsilon }_0}$)

Two electric dipoles of moment $P$ and $64 P$ are placed in opposite direction on a line at a distance of $25 \mathrm{cm}$. The electric field will be zero at point between the dipoles whose distance from the dipole of moment $P$ is

Two point charges $+Q$ and the $-2Q$ are fixed on the $x$ axis at positions $a$ and $2a$ from origin respectively. At what positions on the $x$axis, the resultant electric field is zero.

An electric dipole is kept on the axis of a uniformly charged ring at distance $\frac{R}{\sqrt{2}}$ from the centre 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 radius of the ring is $R$. The force on the dipole is

Two short dipoles $p \hat{\mathrm{k}}$ and $\frac{p}{2} \hat{\mathrm{k}}$ are located at $(0, 0, 0)$ and $(1 \mathrm{m}, 0, 2 \mathrm{m})$, respectively. The resultant electric field due to the two dipoles at the point $(1 \mathrm{m}, 0, 0)$ is

The total electric force on an electric dipole placed in the electric field of a point charge is,

The locus of the points (in the $xy$-plane) where the electric field due to a dipole (dipole axis is along $x$-axis and its equatorial is along $y$-axis) is perpendicular to its axis is