Question 413: Electrostats & Capacitance

Question

A dipole comprises of two charged particles of identical magnitude $$q$$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$$l$$'. If the dipole is placed in a uniform electric field '$$\bar{E}$$'; in such a way that dipole axis makes a very small angle with the electric field, '$$\bar{E}$$'. The angular frequency of the oscillations of the dipole when released is given by:

Accepted Answer

If released, it will oscillate about centre of mass.
For small ' $	heta$ '
$$
\begin{aligned}
& 	au=-\mathrm{PE} . 	heta \\
& \Rightarrow\left[2 \mathrm{~m} \frac{1^2}{9}+\mathrm{m} \frac{4 \mathrm{l}^2}{9}ight] \alpha=-\mathrm{qlE} \cdot 	heta \\
& \Rightarrow \frac{2 \mathrm{ml}^2}{3} \alpha=-\mathrm{qlE} \cdot 	heta \Rightarrow \alpha=-\frac{3 \mathrm{qE}}{2 \mathrm{ml}} 	heta \\
& \omega=\sqrt{\frac{3 \mathrm{qE}}{2 \mathrm{ml}}}
\end{aligned}
$$

Answer

$$\sqrt{\frac{3 q E}{2 m l}}$$

Answer

$$\sqrt{\frac{4 q E}{m l}}$$

Answer

$$\sqrt{\frac{8 q E}{3 m l}}$$

Answer

$$\sqrt{\frac{8 q E}{m l}}$$

Electrostats & Capacitance

Choose the correct answer: