If a proton moves through a potential difference of $4.5 \mathrm{kV}$ what is the magnitude of the change in the proton's potential energy expressed in the unit electron-volt?

In Fig. (a), a particle of elementary charge $+e$ is initially at coordinate $z=20 \mathrm{nm}$ on the dipole axis (here a $z$ axis) through an electric dipole, on the positive side of the dipole. (The origin of $z$ is at the center of the dipole.) The particle is then moved along a circular path around the dipole center until it is at coordinate $z=-20 \mathrm{nm},$ on the negative side of the dipole axis. Figure (b) gives the work $W_{\mathrm{a}}$ done by the force moving the particle versus the angle $\theta$ that locates the particle relative to the positive direction of the $z$ axis. The scale of the vertical axis is set by $W_{\mathrm{as}}=2.0\times {10}^{-30} \mathrm{J}$. What is the magnitude of the dipole moment?

(a)                                                                (b)

When an electron moves from $A$ to $B$ along an electric field line in figure. The electric field does $4.78\times {10}^{-19} \mathrm{J}$ of work on it. What are the electric potential differences (a) $V_B-V_A,$ (b)$V_C-V_A,$ and (c) $V_C-V_B?$

In Figure, a charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance $d=2.00 \mathrm{mm}.$ The plate potentials are $V_1=-80.0 \mathrm{V}$ and $V_2=-50.0 \mathrm{V}$. The particle is slowing from an initial speed of $200 \mathrm{km} {\mathrm{s}}^{-1}$ at the left plate.

(a) Is the particle an electron or a proton?
(b) What is its speed just as it reaches the plate $2?$

A positron (charge $+e$ mass equal to the electron mass) is moving at $1.5\times {10}^7 \mathrm{m} {\mathrm{s}}^{-1}$ in the positive direction of an $x$-axis when, at $x=0,$ it encounters an electric field directed along the $x$-axis. The electric potential $V$ associated with the field is given in the figure. The scale of the vertical axis is set by $V_{\mathrm{s}}=500.0 \mathrm{V}$ (a) Does the positron emerge from the field at $x=0$ (which means its motion is reversed) or at $x=0.50 \mathrm{m}$ (which means its motion is not reversed)? (b) What is its speed when it emerges?

Suppose $N$ electrons can be placed in either of two configurations. In configuration $1,$ they are all placed on the circumference of a narrow ring of radius $R$ and are uniformly distributed so that the distance between adjacent electrons is the same everywhere. In configuration $2\text{,} N-1$ electrons are uniformly distributed on the ring and one electron is placed in the center of the ring.

(a) What is the smallest value of $N$ for which the second configuration is less energetic than the first?

(b) For that value of considering anyone circumference electron, call it $e{}_0.$ How many other circumference electrons are closer to $e_0$ than the central electron is?

The smiling face of the given figure consists of three items:

1. A thin rod of charge $-3.0 \mu C$ that forms a full circle of radius $6.0 \mathrm{cm}$.
2. A second thin rod of charge $1.0 \mu \mathrm{C}$ that forms a circular arc of radius $4.0 \mathrm{cm},$ subtending an angle of $90°$ about the centre of the full circle.
3. An electric dipole with a dipole moment that is perpendicular to a radial line and has a magnitude of $1.28\times {10}^{-21} \mathrm{C} \mathrm{m}$.

What is the net electric potential at the centre?