The surface of a planet is found to be uniformly charged. When a particle of mass $m$ and no charge is thrown at an angle from the surface of the planet,it has a parabolic trajectory as in projectile motion with horizontal range $L$. $A$ particle of mass $m$ and charge $q$,with the same initial conditions,has a range $L/2$. The range of a particle of mass $m$ and charge $2q$,with the same initial conditions,is:

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. It is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma$. If a point charge $q_A$ is placed at the center and another point charge $q_B$ is placed at a distance $c (> b)$ from the center of the shell,then choose the correct statement.

The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

Four charges $Q_1, Q_2, Q_3$, and $Q_4$ of the 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 regarding the signs of these charges are given in List-$I$. The direction of the net force on the charge $q$ is given in List-$II$. Match List-$I$ with List-$II$ and select the correct answer using the codes 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	$4. -y$

$A$ long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like the figure given in:

$A$ negative point charge is placed at point $A$ as shown in the figure. The charge is: