Relation between Field and Potential

Choose the incorrect statement

(1)The potential energy per unit positive charge in an electric field at some point is called the electric potential.

(2) the work required to be done to move a point charge from one point to another in an electric field depends on the position of the points.

(3) the potential energy of the system will increase if a positive charge is moved against the Coulomb force.

(4) None of the above.

You are to bring two charges$q_1\& q_2$ from infinity to the points represented by the potentials $V_1$and $V_2$ in an electric field $\overrightarrow{E}$. If the distance between $q_{1 }\& q_2$ within the field $E$ is $r$, find the total work done in assembling the configuration. Imagine an electric field $\overrightarrow{E} = (20\hat{i} + 30\hat{j}) \mathrm{N} {\mathrm{C}}^{-1}$in a space. The potential at the origin is zero. Find the potential at the point $(2,2) \mathrm{m}$. 

The potential of the field inside a charged sphere depends upon the distance from its centre the point under consideration in the following way: $V=a{r}^n+ b,$ where $a$ and $b$ are constants If the charge is uniformly distributed within the sphere, then the value of $n$ is

From a point if we move in a direction making an angle & measured from $+ve$ $x$ axis, the potential gradient $dv$ is given as $2\cos \theta$. Find the direction and magnitude of electric field at that point.

If electric field strength at a point is zero at a given point, then what can you say about the electric potential at that point? Explain.

Gap between two electrodes of the spark- plug used in an automobile engine is
$1.25 \mathrm{mm}.$ Magnitude of electric field between the electrodes is $1.2\times {10}^4 \mathrm{V} {\mathrm{m}}^{-1}$.Calculate the potential applied across the gap.

The electric potential in a certain situation is found to depend on $x$ only and is given by $v\left(x\right)= ax-b{x}^2$. Find the position on the $x-$axis where the electric intensity is zero.

Statement (A): Inside a charged hollow metal sphere, $E=0, V\ne 0$. ($E$- electric field, $V$-eslectric potential)

Statement (B): The work done in moving a positive charge on an equipotential surface is zero.

Statement (C): When two like charges are brought closer, their mutual electrostatic potential energy will increase.

A uniform electric field of $60 \mathrm{V} {\mathrm{m}}^{-1}$ is directed at $30°$ with the positive $x$-axis as shown in figure. If $OA=3 \mathrm{m}$, then potential difference $V_O-V_A$ is

The electric field in a region is given by $\overrightarrow{E}=\left(3x^{2}y\hat{i}+x^3\hat{j}\right) \mathrm{V} {\mathrm{m}}^{-1}$. The potential difference between the points $A\left(0,0,0\right)$ and $B\left(1\mathrm{m},1\mathrm{m},1\mathrm{m}\right)$ is i.e., $\left(V_A-V_B\right)$

Two infinitely long straight wires having linear charge densities $+2\lambda$ and $-\lambda$ are separated by a distance $4a$ (see figure). The potential difference $V_P-V_Q$ is

The variation of potential $\left(V\right)$ with distance $\left(r\right)$ is shown. Draw the corresponding $\overrightarrow{E}$ with distance

Find potential difference $V_{AB}$ between $A\left(0,0,0\right)$ and $B\left(1 \mathrm{m},1 \mathrm{m},1 \mathrm{m}\right)$ in an electric field 

(a) $\mathrm{E}=y\hat{ı}+x\hat{ȷ}$

Electric field at a distance $x$ from given as $E=\frac{\left(100 \mathrm{N}-{\mathrm{m}}^2/\mathrm{C}\right)}{\left(x^2\right)}$. Then potential difference between the points situated at $x=10 \mathrm{m}$ and $x=20 \mathrm{m}$.

A uniform electric field exists in $x-y$ plane. The potential of points $A\left(+2 \mathrm{m},2 \mathrm{m}\right),B\left(-2 \mathrm{m},2 \mathrm{m}\right)$ and $C\left(2 \mathrm{m},4 \mathrm{m}\right)$ are $4 \mathrm{V},16 \mathrm{V}$ and $12 \mathrm{V}$, respectively. The electric field is

In the figure shown, the electric field intensity at $r=1\mathrm{m}, r=6\mathrm{m}, r=9\mathrm{m}$ in ${\mathrm{Vm}}^{-1}$ is

Distance between to identical plates charged oppositely is $20 \mathrm{cm}$. The electron at the midpoint between the plates experience of a force of $1.6\times {10}^{-15} \mathrm{N}$ The potential difference between the plates is

When we calculate the expression of electric field of any shape we take $\mathrm{d}x$ at $x$ distance, so what do we mean by it and why cannot we take $dt$ at $x$ distance?

A charge $2\times {10}^{-3} \mathrm{C}$ and the mass $1 \mathrm{gm}$ is projected from level ground with a velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of with the $37°$, horizontal ($x$ direction). The electric potential in space is given by, $V=3x+4y$. What is the speed of the charge (in $\mathrm{m} {\mathrm{s}}^{-1}$ ) when its $y$, coordinate is maximum?

Two points $A$ and $B$ are at distances of $\text{'}a\text{'}$ and $\text{'}b\text{'}$ respectively from an infinite conducting plate having charge density $\sigma$. The work done in moving charge $Q$ from $A$ to $B$ is