Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V₀ and the top plate at $$-$$V₀. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)


The average current in the steady state registered by the ammeter in the circuit will be

Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then

Four charges Q₁, Q₂, Q₃ and Q₄ of same magnitude are fixed along the x axis at x = $$-$$2a, $$-$$a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

List I		List II
P.	Q$$_1$$, Q$$_2$$, Q$$_3$$, Q$$_4$$ all positive	1.	+x
Q.	Q$$_1$$, Q$$_2$$ positive; Q$$_3$$, Q$$_4$$ negative	2.	$$ - $$x
R.	Q$$_1$$, Q$$_4$$ positive; Q$$_2$$, Q$$_3$$ negative	3.	+y
S.	Q$$_1$$, Q$$_3$$ positive; Q$$_2$$, Q$$_4$$ negative	4.	$$ - $$y

Two non-conducting solid spheres of radii $$R$$ and $$2R,$$ having uniform volume charge densities $${\rho _1}$$ and $${\rho _2}$$ respectively, touch each other. The net electric field at a distance $$2$$ $$R$$ from the center of the smaller sphere, along the line joining the centers of the spheres, is zero. The ratio $${{{\rho _1}} \over {{\rho _2}}}$$ can be