Two charges of equal magnitude '$$q$$' are placed in air at a distance '$$2 r$$' apart and third charge '$$-2 \mathrm{q}$$' is placed at mid point. The potential energy of the system is $$\left(\varepsilon_0=\right.$$ permittivity of free space)

An electron moving with velocity $$1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$$ has wavelength of $$0.4 \mathop A\limits^o$$. The required accelerating voltage for the electron motion is [charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$, mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$ ]

Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $$Q$$ in terms of $$q$$ is

The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $$\mathrm{g}>\mathrm{qE} / \mathrm{m}$$ )