Electric Potential

Figure shows two co-axial rings of radius $R_1$ and $R_2$ having charges $Q_1$ and $Q_2$. Their centres are separated by distance $h$. Find potential at the midpoint of line segment joining of centres of the two rings.

A unit charge is moved in a circular path of radius $r$ having a point charge $q$ at the centre. The work done in one complete rotation is

Assertion: Electrons move from a region of higher potential to a region of lower potential.

Reason: An electron has less potential energy at a point where potential is higher and vice-versa.

Assertion: Electrons move away from a region of lower potential to a region of higher potential.

Reason: Since an electron has negative charge.

Assertion: The potential of a conductor depend upon the charge given to it.

Reason: Potential depend on charge as well as shape and size of conductor also.

Assertion: When two charge particles are moved away from each other, then their electric potential energy must decrease.
Reason: For two point charges $q_1$ and $q_2$ at separation $r$, electric potential energy is $\frac{k{q}_1{q}_2}{r}$.

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

$15\mathrm{ }\text{joule}$ of work has to be done against an existing electric field to take a charge of $0.01\mathrm{ }\mathrm{C}$ from $A$ to $B$. Then the potential difference $\left({\mathrm{V}}_{\mathrm{B}}-\mathrm{ }{\mathrm{V}}_{\mathrm{A}}\right)$ is 

Two insulated charged spheres of radii $20\mathrm{ }\mathrm{c}\mathrm{m}$ and $25\mathrm{ }\mathrm{c}\mathrm{m}$ respectively, and having an equal charge $\mathrm{Q}$, are connected by a copper wire. Then they are separated. Which of the following is correct?

When two uncharged metal balls, each of radius $0.09\mathrm{ }\mathrm{m}\mathrm{m}$, collide, two electrons are transferred between them. The potential difference between them would be

When a body is connected to the earth, then electrons from the earth flow into the body. It means that the body is

The electric potential at point $A$ is $20\mathrm{ }\mathrm{V}$ and at $B$ is $-20\mathrm{ }\mathrm{V}$. The work done by an external force, in moving an electron slowly from $B$ to $A$, is

Eight charges, each of the magnitude $q$, are placed at the vertices of a cube, placed in vacuum. Electric potential at the centre of the cube, due to this system of charges, is
(${\epsilon }_0$ is permittivity of vacuum and $a$ is the length of each side of the cube).

An electric charge ${10}^{-3}\mathrm{ }\mathrm{\mu }\mathrm{C}$ is placed at the origin $\left(0,\mathrm{ }0\right)$ of an $\mathrm{X}\text{-}\mathrm{Y}$ co-ordinate system. Two points, $A$ and $B$, are situated at $\left(\sqrt{2}, \sqrt{2}\right)$ and $\left(2, 0\right)$, respectively. The potential difference between the points $A$ and $B$ will be

On moving a charge of $2 \mathrm{C}$ from point $A$, where the potential is $+12 \mathrm{V}$, to point $B$, where the potential is $-12\mathrm{ }\mathrm{V}$, the work done is

An electric field is spread uniformly in $\mathrm{Y}$-axis. Consider a point $\mathrm{A}$ as origin point. The co-ordinates of point $\mathrm{B}$ are equal to $(0,\mathrm{ }2)\mathrm{m}$. The co-ordinates of point $\mathrm{C}$ are $(2,\mathrm{ }0)\mathrm{m}$. At points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$, electric potentials are ${\mathrm{V}}_{\mathrm{A}},\mathrm{ }{\mathrm{V}}_{\mathrm{B}}$ and ${\mathrm{V}}_{\mathrm{C}}$ respectively. From the following options, which is correct?

The electric potential at point $\mathrm{A}$ is $20\mathrm{ }\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}\mathrm{s}$ and $\mathrm{B}$ is $–\mathrm{ }20\mathrm{ }\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}\mathrm{s}$. The work done by an external force in moving electron slowly from $\mathrm{B}$ to $\mathrm{A}$ is -

Two concentric spheres (hollow) are shown in diagram. What charge should be given to the smaller sphere so that potential at point $\mathrm{P}$ outside the sphere is zero ? $(\mathrm{I}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{s}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}\mathrm{ }=\mathrm{ }\mathrm{r},\mathrm{ }\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{s}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}\mathrm{ }=\mathrm{ }\mathrm{R}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{o}\mathrm{n}\mathrm{ }\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{s}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{ }=\mathrm{ }\mathrm{Q})$ :
 

On moving a charge of $2 \mathrm{C}$ from a point $A$, where potential is $+12 \mathrm{V}$ to a point $B$, where potential is $–12\mathrm{ }\mathrm{V}$, the work done is

A point charge $q$ moves from point $P$ to point $S$ along the path $PQRS$ in a uniform electric field $\overrightarrow{\mathrm{E}}$ pointing parallel to the positive direction of the $x-$axis, figure. The coordinates of the points $P,Q,R$ and $S$ are $\left(a, b, 0\right)$, $\left(2a, 0, 0\right)$, $\left(a, -b, 0\right)$ and $\left(0, 0, 0\right)$, respectively. The work done by the field in the above process is given by the expression