Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is
$\frac{q}{{2{\pi ^2}{\varepsilon _0}{R^2}}}$
$\frac{q}{{4{\pi ^2}{\varepsilon _0}{R^2}}}$
$\frac{q}{{4\pi {\varepsilon _0}{R^2}}}$
$\frac{q}{{2\pi {\varepsilon _0}{R^2}}}$
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 slightly from the equilibrium position, then the angular frequency of its oscillations is
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
The electric potential $V$ at any point $(x,y,z)$ in space is given by equation $V = 4x^2\,volt$ where $x, y$ and $z$ are all in metre. The electric field at the point $(1\,m, 0, 2\,m)$ in $V/m$ is
A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the electrical force on $Q$ is zero, then $Q/q$ equals
A point charge $q$ is placed at a distance $\frac{a}{2}$ directly above the centre of a square of side $a$ . The electric flux through the square is