$A$ rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0\hat{i}$. If another electric field $\vec{E}_2 = 2E_0(\hat{j} + \hat{k})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate) (in $\%$)?

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of an $x-y$ coordinate system. Then:

When does the torque acting on an electric dipole in a uniform electric field become zero?

Five identical small electric dipoles are placed at a distance $r$ from an infinitely long straight wire carrying a uniform charge density $\lambda$. If they experience forces of magnitude $F_1, F_2, F_3, F_4$ and $F_5$ respectively,then:

An electric dipole of length $3 \text{ cm}$ is placed with its axis making an angle of $60^\circ$ with a uniform electric field of $5 \times 10^4 \text{ N/C}$. It experiences a torque of $9\sqrt{3} \text{ Nm}$. The magnitude of charge on the dipole is $(\sin 60^\circ = \frac{\sqrt{3}}{2})$

An electrical dipole coincides on the $z$-axis and its midpoint is at the origin of the coordinate system. The electric field at an axial point at a distance $z$ from the origin is $\vec{E}(z)$ and the electric field at an equatorial point at a distance $y$ from the origin is $\vec{E}(y)$. Here $z = y \gg a$,so $\left| \frac{\vec{E}(z)}{\vec{E}(y)} \right| = . . . . . . . .$.