A charge of uniform linear density $1.5 \mathrm{nC} {\mathrm{m}}^{-1}$ is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius$=5.0 \mathrm{cm}$ and outer radius$=10 \mathrm{cm}$). The net charge on the shell is zero.

$\left(A\right)$ What is the magnitude of the electric field $15 \mathrm{cm}$ from the axis of the shell?

What is the surface charge density on the

$\left(B\right)$ inner surface of the shell?

$\left(C\right)$ outer surface of the shell?

The figure gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by $E_s=10\times {10}^7 \mathrm{N} {\mathrm{C}}^{-1}$. $\left(a\right)$ What is the charge on the sphere? $\left(b\right)$ What is the field magnitude at $r=8.0 \mathrm{m}?$

ln the figure, two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have excess surface charge densities of opposite signs and magnitude $2.31\times {10}^{-22} \mathrm{C} {\mathrm{m}}^{-2}.$ In unit vector notation, what is the electric field at points,$\left(a\right)$ to the left of the plates,
$\left(b\right)$ to the right of them and $\left(c\right)$ between them?

In figure a small circular hole of radius $R=1.30 \mathrm{cm}$ has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density$\text{σ}=4.50 \mathrm{pC} {\mathrm{m}}^{-2}$. A $z$-axis, with its origin at the hole's center, is perpendicular to the surface. In unit vector notation, what is the electric field at point $P$ at $z=2.56 \mathrm{cm}$?

In figure, a nonconducting spherical shell of inner radius $a=1.50 \mathrm{cm}$ and outer radius $b=2.40 \mathrm{cm}$ has (within its thickness) a positive volume charge density $\text{ρ}=A/r$ where $A$ is constant and $r$ is the distance from the center of the shell. In addition, a small ball of charge $75.0 \mathrm{fC}$ is located at that center. What value should $\mathrm{A}$ have if the electric field in the shell $(a\le r\le b)$ is to be uniform?

The figure shows a very large nonconducting sheet that has a uniform surface charge density of $\sigma =-2.00 \mu \mathrm{C} {\mathrm{m}}^{-2}$; it also shows a particle of charge $Q=8.00 \mu \mathrm{C},$ at distance $d$ from the sheet. Both are fixed in place. If $d=0.200 \mathrm{m},$ at what $\left(a\right)$ positive and $\left(b\right)$ negative coordinate on the $x$ axis (other than infinity) is the net electric field ${\overrightarrow{E}}_{\text{net }}$ of the sheet and particle zero? $\left(c\right)$ If $d=0.950 \mathrm{m},$ at what coordinate on the $x$ axis is ${\overrightarrow{E}}_{\text{net }}=0?$

Figure shows a section of a long, thin-walled metal tube of radius $R=2.50 \mathrm{cm},$ with a charge per unit length of $\lambda =2.00\times {10}^{-8} \mathrm{C} {\mathrm{m}}^{-1}$. What is the magnitude $E$ of the electric field at radial distance (a) $r=\frac{R}{2.00}$ and (b) $r=2.00 R?$ (c) Graph $E$ versus $r$ for the range $r=0$ to $2.00 R$.