Two long, charged, thin-walled, concentric cylindrical shells have radii of $3.0 \mathrm{cm}$ and $6.0 \mathrm{cm}$. The charge per unit length is $-7.0\times {10}^{-6} \mathrm{C} {\mathrm{m}}^{-1}$ on the inner shell and $+5.0\times {10}^{-6} \mathrm{C} {\mathrm{m}}^{-1}$ on the outer shell. What is the (a) magnitude $E$ and (b) direction (radially inward or outward) of the electric field at radial distance $r=4.0 \mathrm{cm}$? What is (c) $E$ and (d) the direction at $r=8.0 \mathrm{cm}$?

The figure shows a spherical shell with uniform volume charge density $\rho =1.56 \mathrm{nC} {\mathrm{m}}^{-3}$, inner radius $a=10.0 \mathrm{cm}$, and outer radius $b=2.00a$. What is the magnitude of the electric field at radial distances (a) $r=0$, (b) $r=a/2.00$, (c) $r=a$, (d) $r=1.50a$, (e) $r=b$ and (f) $r=3.00b$?

In the figure shown below, a solid sphere of radius $a=2.00 \mathrm{cm}$ is concentric with a spherical conducting shell of inner radius $b=2.00 a$ and outer radius $c=2.40 a$. The sphere has a net uniform charge $q_1=+2.00 \mathrm{fC}$; the shell has a net charge $q_2=-q_1$. What is the magnitude of the electric field at radial distances (a) $r=0,$ (b) $r=\frac{a}{2.00},$ (c) $r=a$ (d) $r=1.50a$ (e) $r=2.30a,$ and (f) $r=3.50a?$ What is the net charge on the (g) inner and (h) outer surface of the shell?

In the fig. a butterfly net is in a uniform electric field of magnitude $E=4.5 \mathrm{mN} {\mathrm{C}}^{-1}$. The rim, a circle of radius $a=11 \mathrm{cm}$ is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the net.

Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are non-conducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component $E$ of the electric field versus radial distance $r$ from the common axis, and $E_s=6.0\times {10}^3 \mathrm{N} {\mathrm{C}}^{-1}$ What is the shell's linear charge density?

$\left(\mathrm{a}\right) \left(\mathrm{b}\right)$

The box-like Gaussian surface shown in the fig. encloses a net charge of $+32 {\epsilon }_0 \mathrm{C}$ and lies in an electric field given by $\overrightarrow{E}=\left[\left(10.0+2.00x\right)\hat{\mathrm{i}}-3.00\hat{\mathrm{j}}+bz\hat{\mathrm{k}}\right] \mathrm{N} {\mathrm{C}}^{-1},$ with $x$ and $z$ in meters and $b$ a constant. The bottom face is in the $xz$ plane; the top face is in the horizontal plane passing through $y_2=1.00 \mathrm{m}$ . For$x_1=1.00 \mathrm{m} ,x_2=4.00 \mathrm{m}, z_1=1.00 \mathrm{m}$ and $z_2=3.00 \mathrm{m},$ what is the value of $b?$