A flat slab of nonconducting material has thickness $2 d$, which is small compared to its height and breadth. Define the $x$ axis to be along the direction of the slab's thickness with the origin at the center of the slab. If the slab carries a volume charge density $\rho_{\mathrm{E}}(x)=-\rho_0$ in the region $-d \leq x<0$, and $\rho_{\mathrm{E}}(x)=+\rho_0$ in the region $0<x \leq+d$, determine the electric field $\overrightarrow{\mathbf{E}}$ regions $\text{(b) } 0<x \leq+d$. Let $\rho_0$ be a positive constant.

A slab of insulating material has thickness $2d$ and is oriented so that its faces are parallel to the yz-plane and given by the planes $x = d$ and $x = -d$. The $y-$ and $z-$dimensions of the slab are very large compared to $d$; treat them as essentially infinite. The slab has a uniform positive charge density $\rho$.

Explain why the electric field due to the slab is zero at the center of the slab $(x = 0)$.

A flat slab of nonconducting material carries a uniform charge per unit volume, $\rho_{\mathrm{E}}$. The slab has thickness $d$ which is small compared to the height and breadth of the slab. Determine the electric field as a function of $x$ (a) inside the slab. Take the origin at the center of the slab.

The electric field $\overrightarrow{\mathbf{E}}$ is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface?

The electric field $\overrightarrow{\mathbf{E}}$ is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface?

The total electric flux from a cubical box 28.0 cm on a side is $1.45 \times 10^{3} \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}$. What charge is enclosed by the box?

Suppose two thin flat nonconducting plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 25 \mu \mathrm{C}$. Estimate the total force exerted by one plate on the other (ignore edge effects).

Suppose two thin flat nonconducting plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 25 \mu \mathrm{C}$. How much work would be required to move the plates from $5.0 \mathrm{~mm}$ apart to $1.00 \mathrm{~cm}$ apart?

Suppose two thin flat plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 15 \mu \mathrm{C}$. (b) How much work would be required to move the plates from $5.0 \mathrm{~mm}$ apart to $1.00 \mathrm{~cm}$ apart?

Suppose two thin flat plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 15 \mu \mathrm{C}$. (a) Estimate the total force exerted by one plate on the other (ignore edge effects).

Suppose two thin flat nonconducting plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 25 \mu \mathrm{C}$. Estimate the total force exerted by one plate on the other (ignore edge effects).

Suppose the density of charge between $r_1$ and $r_0$ of the hollow sphere of Problem 29 (Fig. 22-32) varies as $\rho_{\mathrm{E}}=\rho_0 r_1 / r$. Determine the electric field as a function of $r$ for (d) Plot $E$ versus $r$ from $r=0$ to $r=2 r_0$.

Suppose the nonconducting sphere has a spherical cavity of radius $r_1$ centered at the sphere's center.The outer radius of sphere is $r_0$. The density of charge between $r_1$ and $r_0$ varies as a function of $r$ as $\rho_{\mathrm{E}}=\rho_0 r_1 / r$. Determine the electric field as a function of $r$ for $(c) r>r_0$.

Suppose the nonconducting sphere has a spherical cavity of radius $r_1$ centered at the sphere's center.The outer radius of sphere is $r_0$. The density of charge between $r_1$ and $r_0$ varies as a function of $r$ as $\rho_{\mathrm{E}}=\rho_0 r_1 / r$. Determine the electric field as a function of $r$ for

(b) $r_1<r<r_0$.