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?

In the given figure, what is the net electric potential at point $P$ due to the four particles if $V=0$ at infinity, $q=7.50 \mathrm{fC},$ and $d=1.60 \mathrm{cm}?$

In the given figure, how much work must we do to bring a particle, of charge $Q=+12e$ and initially at rest, along the dashed line from infinity to the indicated point near two fixed particles of charges $q_1=+4e$ and $q_2=-\frac{q_1}{2}?$ Distance $d=1.40 \mathrm{cm}, {\theta }_1=43°,$ and ${\theta }_2=60°$.

The particles shown in the figure each have a charge magnitude $q=5.00 \mathrm{pC}$ and the charges were initially infinitely far apart. To form the square with edge length $a=64.0 \mathrm{cm},$ (a) how much work must be done by an external agent, (b) how must work be done by the electric forces, and (c) what is the potential energy of the system?