Consider an electron travelling with a speed v_o and entering into a uniform electric field \(\vec{E}\) which is perpendicular to \(\vec { { v }_{ 0 } } \) as shown in the Figure. Ignoring gravity, obtain the electron’s acceleration, velocity and position as functions of time.

The electrostatic potential is given as a function of x in figure (i) and (ii). (a) Calculate the corresponding electric fields in regions A, B, C and D for the Figure (i). (b) Plot the electric field as a function of x for the figure (ii).

A point charge of +10 μC is placed at a distance of 20 cm from another identical point charge of +10 μC. A point charge of -2 μC is moved from point a to b as shown in the figure. Calculate the change in potential energy of the system? Interpret your result.

An electron and a proton are allowed to fall through the separation between the plates of a parallel plate capacitor of voltage 5 V and separation distance h = 1 mm as shown in the figure.

(a) Calculate the time of flight for both electron and proton
(b) Suppose if a neutron is allowed to fall, what is the time of flight?
(c) Among the three, which one will reach the bottom first? (Take m_p = 1.6 x 10^-27 kg, m_e = 9.1 x 10^-31 kg and g = 10 m s^-2)

For the given capacitor configuration
(a) Find the charges on each capacitor
(b) potential difference across them
(c) energy stored in each capacitor