K K Sharma Solutions for Chapter: Electric Charges and Fields, Exercise 1: TOPICWISE QUESTIONS

The magnitude of electric field intensity at point $(2,0,0)$ due to a dipole of dipole moment $\overrightarrow{\mathit{p}}=\hat{\mathrm{i}}+\sqrt{3}\hat{\mathrm{j}}$ kept at origin is (where, $k=\frac{1}{4\mathrm{\pi }{\epsilon }_0}$)

Two coaxial dipoles of dipole moments $p_1$ and $p_2$ are separated by a distance $r.$ The magnitude of electric force on $p_1$ due to $p_2$ is $\left(k=\frac{1}{4\mathrm{\pi }{\epsilon }_0}\right)$

Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point $O$ and perpendicular to the plane of the figure as a function of distance $x$ from point $O$ is (assume $x>>a$)

A dipole is kept near an infinite line of charge. If the net force on the dipole is zero, then its dipole moment is

An electric dipole is placed in a uniform electric field $\overrightarrow{E}$ of magnitude $40 \mathrm{N} {\mathrm{C}}^{-1}$. The graph below shows the magnitude of the torque on the dipole versus the angle $\mathrm{\theta }$ between the field $\overrightarrow{E}$ and the dipole moment $\overrightarrow{p}$. The magnitude of dipole moment $\overrightarrow{p}$ is equal to

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

An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I$. If the dipole is displaced, then the angular frequency of its oscillation is

A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a uniform vertical electric field $E.$ The value of $E$ is