An electric dipole is placed along the $x$ -axis at the origin $O.$ A point $P$ is at a distance of $20\, cm$ from this origin such that $OP$ makes an angle $\frac{\pi}{3}$ with the $x$ -axis. If the electric field at $P$ makes an angle $\theta$ with the $x$ -axis, the value of $\theta$ would be
$\frac{\pi}{3}$
$\frac{\pi}{3} + \tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$
$\frac{2 \pi}{3}$
$\tan^{-1} \,\left( {\frac{{\sqrt 3 }}{2}} \right)$
Calculate the work done in taking a charge $-2 \times 10^{-9} \,C$ from $A$ to $B$ via $C$ is ......... (in diagram)
A parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. A slab of dielectric is then inserted between the plates. Which of the following three quantities change?
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$ , it has the same (total) energy stored in it, as the first combination has. The value of $C_2$ , in terms of $C_1$, is then
As shown in the fig. charges $+\,q$ and $-\,q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is
A point charge $'q'$ is placed at a point inside a hollow conducting sphere. Which of the following electric force pattern is correct ?