Two identical point charges are placed at a separation of $ l.$ $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?

The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$, then

Potential in the $x-y$ plane is given as $V = 5(x^2 + xy)\, volts$. The electric field at the point $(1, -2)$ will be

Electric potential at an equatorial point of a small dipole with dipole moment $P$  ( $r$ , distance from the dipole) is

A charged object is launched inside a time varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$ , its position vector $\vec r$, velocity $\vec v$ and acceleration $\vec a$ are measured. A student watches the video at a later time but mistakenly plays the tape in the reverse direction. What is the position, velocity, and acceleration of the object, at moment $A$ observed by the student respectively?

A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It  remains in equilibrium on a rough inclined plane in the presence of uniform horizontal  electric field $E =$