$A$ particle of mass $m$ and charge $q$ is thrown in a region where uniform gravitational field and electric field are present. The path of the particle:

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its center is represented by which of the following graphs?

$A$ positively charged thin metal ring of radius $R$ is fixed in the $xy$-plane with its centre at the origin $O$. $A$ negatively charged particle $P$ is released from rest at the point $(0, 0, z_0)$,where $z_0 > 0$. Then the motion of $P$ is:

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 identical charged spheres suspended from a common point by two massless strings of lengths $l$ are initially at a distance $d$ $(d << l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres,as:

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting, which of the following statements is true?