Electric Potential

A particle of charge+q and mass m moving under the influence of a uniform electric field E $\widehat{\text{i}}\text{and magnetic field B}\widehat{\text{k}}$enters in I quadrant of a coordinate system at a point (0, a) with initial velocity v$\widehat{\text{i}}$and leaves the quadrant at a point (2a, 0) with velocity $-\mathrm{2 }\text{v}\widehat{\text{j}}$.
Find Rate of work done by the electric field at point (0, a)

How does the electric potential due to a dipole vary on the dipole axis as a function of $r$– distance of the field point from the mid–point of the dipole, at large distances?

Two charges each of $+ 40 \mathrm{\mu C}$ are placed at a distance of $0.4 \mathrm{m}$. Calculate the potential at the mid-point. Dielectric constant of the medium is $2$.

Compute $V_A-V_B$in Figure (a) and (b). The charge $q$ is $+1.0\times {10}^{-6} \mathrm{C}$.

                              (a)                                                                                                (b)

Calculate the amount of work done in bringing a point-charge of $8 \mathrm{\mu C}$ from point A to B if electrical potentials are $2 \mathrm{volt}$ and $4 \mathrm{volt}$ respectively at A and B.

An uncharged conducting sphere is placed near to a charge $+q$ as shown in the figure. The distance between charge $+q$ and the sphere is d. Find the magnitude of the electric field produced by induced charge at the centre of the sphere. 

In a certain field, the potential energy is $U= a{x}^{2 }-b{x}^3$, where$a$ and $b$constants. The particle is in stable equilibrium at $x$equal to

If $200 \mathrm{J}$ of work must be done to move electric charge of $8 \mathrm{C}$ from a place where
potential is $-10 \mathrm{V}$ to another place where electric potential is $V\mathit{ }$volt. Find the value of$V\mathit{.}$

A point charge$q$is a distance r from the centre $O$ of an uncharged spherical conducting layer, whose inner and outer radii are equal to $a$ and $b$ respectively. Find the potential at the point$O$if $r<a$

What is the potential difference between the conductors A and B shown in the below figure? If the conductors are connected by a length of wire, which way will electrons flow? When will this flow of electrons stop?

Does electric potential exist in the absence of work done?

Dimensional formula of potential gradient

A battery of $10$ volt carries $20,000 \mathrm{C}$ of charge through a resistance of $20 \mathrm{\Omega }$. The work done in $10$ seconds is

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.

$4 \mathrm{joule}$ work is done to bring $2 \mathrm{C}$ charge from infinity to electric field what is the potential?

If a positive charge is placed at a certain distance from point $P$ which has some electric potential, and then if we increase the distance of point from the positive charge, the potential would decrease. While in case of a negative charge, on increasing the distance, the potential would increase. Justify this.

State differences between electric potential and electric flux.

What is the potential difference between points C and D ?

The unit of electric potential difference is:

Two points A and B are $50 \mathrm{m}$ apart from each other in a uniform electric field of $25 \mathrm{V} {\mathrm{m}}^{-1}$. Calculate the potential difference between the two given points.