An electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is accelerated from rest in a uniform electric field of strength '$$E$$'. The velocity acquired by the electron, when it travels a distance '$$\mathrm{L}$$', is

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All other parameters are unchanged.)

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 $$=9 \times 10^{-31} \mathrm{~kg}$$ ]