(a) Figure $\left(a\right)$ shows a nonconducting rod of length $L=6.00 \mathrm{cm}$ and uniform linear charge density $\lambda =+7.07 \mathrm{pC} {\mathrm{m}}^{-1}$. Assume that the electric potential is defined to be $V$$=0$ at infinity. What is $V$ at point $P$ at a distance $d=8.00 \mathrm{cm}$ along the rod's perpendicular bisector?

(b) Figure $\left(b\right)$ shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude $3.68 \mathrm{pC} {\mathrm{m}}^{-1}$. With $V=0$ at infinity, what is $V$ at $P?$ Is the potential at $P$ positive, negative or zero if $P$ is moved in the plane of the figure by a distance of $\frac{L}{4}$ (c) upward and (d) leftward?

The thin plastic rod of length $L=12.0 \mathrm{cm}$ as shown in figure, has a non-uniform linear charge density $\text{λ}=cx \mathrm{C} {\mathrm{m}}^{-1},$ where, $c=49.9 \mathrm{pC} {\mathrm{m}}^{-2}$ (a) With $V=0$ at infinity, find the electric potential at point $P_2$ on the $y$-axis at $y=D=3.56 \mathrm{cm}.$ (b) Find the electric field component $E_{\mathrm{y}}$ at $P_2$ (c) Why cannot the field component $E_{\mathrm{x}}$ at $P_2$ be found using the result of (a)?

In the figure, particles with the charges $q_1=+15e$ and $q_2=-5e$ are fixed with a separation of $d=24.0 \mathrm{cm}.$ With electric potential defined to be $V=0$ at infinity, what are the finite (a) positive and (b) negative values of $x$ at which the net electric potential on the $x$-axis is zero?

Two particles of charges $q_1$ and $q_2$ are separated by a distance $d$ in the figure. The net electric field due to the particles is zero at $x=d/4.$

(a) With$V=0$ at infinity, locate (in terms of $\mathrm{d}$) any point on the $\mathrm{x}$-axis (other than at infinity) at which the electric potential due to the two particles is zero.

(b) If, instead the net electric potential is $0$ at $x=d/4,$ find (in terms of $d$) the coordinates of any point (other than at infinity) at which the net electric field is zero.

Plastic rod has been bent into a circle of radius $R=8.20 \mathrm{cm}$ It has a charge $Q_1=+7.07 \mathrm{pC}$ uniformly distributed along one quarter of its circumference and a charge $Q_2=-6 Q_1$ is uniformly distributed along the rest of the circumference (as shown in fig.)  With $V=0$ at infinity, what is the electric potential at (a) the center $C$ of the circle and (b) point $P$ on the central axis of the circle at distance $D=2.05 \mathrm{cm}$ from the center?

An electron is placed in an $xy$ plane where the electric potential depends on $x$ and $y$ as shown, for the coordinate axes, in the figure (the potential does not depend on $z$). The scale of the vertical axis is set by $V_{\mathrm{s}}=1000 \mathrm{V}$. In unit-vector notation, what is the electric force on the electron?

The electric potential $V$ in the space between two flat parallel plates $1$ and $2$ is $V=1500 x^2$ (in volts), where, $x$ (in meters) is the perpendicular distance from plate $1.$ At $x=1.8 \mathrm{cm},$

(a) What is the magnitude of the electric field?

(b) Is the field directed towards or away from plate $1?$