A thin non-conducting rod with a uniform distribution of positive charge $Q$ is bent into a complete circle of radius $R$ (as shown in figure). The central perpendicular axis through the ring is a $z$ axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at $\left(\mathrm{a}\right)$ $z=0$ and $\left(\mathrm{b}\right) z=\infty ?$ $\left(\mathrm{c}\right)$ In terms of $R$ at what positive value of $z$ is that magnitude maximum? $\left(\mathrm{d}\right)$ If $R=2.00 \mathrm{cm}$ and $Q=5.00 \mu \mathrm{C},$ what is the maximum magnitude?

Two large parallel Copper plates are $8.0 \mathrm{cm}$ apart and have a uniform electric field between them as depicted in the figure. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and find their distance from the positive plate when they pass each other. (Does it surprise you that you need not know the electric field to solve this problem?) 

Figure shows an uneven arrangement of electrons $\left(e\right)$ and protons $\left(p\right)$ on a circular arc of radius, $r=2.5 \mathrm{cm}$ with angles ${\theta }_1=30.0°, {\theta }_2=50.0°, {\theta }_3=30.0°$ and ${\theta }_4=20.0°$. What are the (a) magnitude and (b) direction (relative to the positive direction of the $r$ axis) of the net electric field produced at the center of the arc?

Figure shows two parallel non-conducting rings with their central axes along a common line. Ring $1$ has uniform charge $q_1$ and radius $R$, ring $2$ has uniform charge $q_2$ and the same radius $R$. The rings are separated by distance, $d=4.00R$. The net electric field at point $P$ on the common line at distance $R$ from ring $1$ is zero. What is the ratio $\frac{q_1}{q_2}$? 

In figure shown below, positive charge, $q=9.25 \mathrm{pC}$ is spread uniformly along a thin non-conducting rod of length, $L=16.0 \mathrm{cm}$. What are the (a) magnitude and (b) direction (relative to the positive direction of the $x$-axis) of the electric field produced at point $P$ at a distance, $R=$$6.00 \mathrm{cm}$ from the rod along its perpendicular bisector?

In figure shown below, two curved plastic rods, one of charge $+q$ and the other of charge $-q$ form a circle of radius, $R=4.25 \mathrm{cm}$ in an $xy$-plane. The $x$-axis passes through both the connecting points and the charge is distributed uniformly on both rods. If $q=15.0 \mathrm{pC}$ , what are the (a) magnitude and (b) direction (relative to the positive direction of the $x$-axis) of the electric field $\overrightarrow{E}$ produced at  $P$ at the center of the circle? 

In the figure, a non-conducting rod of length, $L=8.15 \mathrm{cm}$ has a charge, $-q=-4.23 \mathrm{fC}$ uniformly distributed along its length. (a) What is the linear charge density of the rod? What are the (b) magnitude and (c) direction (relative to the positive direction of the $x$-axis) of the electric field produced at point $P$ at a distance, $a=12.00 \mathrm{cm}$ from the rod? What is the electric field produced at distance, $a=50 \mathrm{m}$ by (d) the rod and (e) a particle of charge, $-q=$ $-4.23 \mathrm{fC}$ that we use to replace the rod? (At that distance, the rod looks like a particle.)

In figure, a thin glass rod forms a semicircle of radius $r=3.00 \mathrm{cm}.$ Charge is uniformly distributed along the rod with$+q=4.50 \mathrm{pC}$ in the upper half and $-q=-4.50 \mathrm{pC}$ in the lower half. What are the $\left(\mathrm{a}\right)$ magnitude and $\left(\mathrm{b}\right)$ direction (relative to the positive direction of the $x$-axis) of the electric field $\overrightarrow{E}$ at $P,$ the center of the semicircle?