$A$ toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\vec E$. Due to the force $q\vec E$,its velocity increases from $0$ to $6\, m s^{-1}$ in one second. At that instant,the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively:

Answer the following:
$(a)$ The top of the atmosphere is at about $400 \; kV$ with respect to the surface of the earth,corresponding to an electric field that decreases with altitude. Near the surface of the earth,the field is about $100 \; Vm^{-1}$. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ $A$ man fixes outside his house one evening a two-metre-high insulating slab carrying on its top a large aluminium sheet of area $1 \; m^2$. Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \; A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words,what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during lightning?

$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

Three charges are placed as shown in the figure. The magnitude of $q_1$ is $2.00\, \mu C$,but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$,and the net force on $q_3$ is entirely in the negative $x-$ direction. As per the condition given,the signs of $q_1$ and $q_2$ will be

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$,the work done will be equal to

Five balls numbered $1$ to $5$ are suspended using separate threads. Pairs $(1, 2), (2, 4)$ and $(4, 1)$ show electrostatic attraction,while pairs $(2, 3)$ and $(4, 5)$ show repulsion. Ball $1$ must be: