Write Gauss's law for the gravitational field $\overrightarrow{\mathbf{g}}$

A point charge of $8.20 \mathrm{nC}$ is located at the origin and a second charge of $-5.00 \mathrm{nC}$ is located on the $x$ axis at $x=2.75 \mathrm{~cm}$. Calculate the electric flux through a sphere centered at the origin with radius $1.00 \mathrm{~m}$. Repeat the calculation for a sphere of radius $2.00 \mathrm{~m}$.

A uniform field $\overrightarrow{\mathbf{E}}$ is parallel to the axis of a hollow hemisphere of radius $r$, as we discussed earlier.

What is the electric flux through the hemispherical surface?

A point charge produces an electric flux of $+235 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}$ through a gaussian sphere of radius $45.0 \mathrm{~cm}$ centered on the charge. What is the magnitude and sign of the charge?

A point charge produces an electric flux of $+235 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}$ through a gaussian sphere of radius $45.0 \mathrm{~cm}$ centered on the charge. What is the flux through a gaussian sphere with a radius $32.5 \mathrm{~cm}$ ?

A $+Q$ point charge is located at the center of a hollow metal sphere. The sphere is also charged, carrying an equal but opposite total charge of $-Q$. Consider the region between the point charge and the inside of the spherical shell. Which statement is true? (a) The electric field is only due to the point charge $\left(E=k Q / r^2\right.$ pointing out $)$ (b) The electric field is zero. $(c)$ The electric field is twice that due to the point charge. (d) The electric field is larger than for the point charge, but not twice as large.

A uniform field $\overrightarrow{\mathbf{E}}$ is parallel to the axis of a hollow hemisphere of radius $r$, as we discussed earlier.

What is the result if $\overrightarrow{\mathbf{E}}$ is instead vertical, perpendicular to the axis, and still uniform?

The total electric flux out from a cubical box of side $21.0 \mathrm{~cm}$ is $1.85 \times 10^3 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}$. What charge is enclosed by the box?

Charge is distributed within a solid sphere of radius $r_0$ in such a way that the charge density is a function of the radial position within the sphere of the form: $\rho_{\mathrm{E}}(r)=\rho_0\left(r / r_0\right)$. If the total charge within the sphere is $Q$ (and positive), what is the electric field everywhere within the sphere in terms of $Q, r_0$, and the radial position $r$ ?

An extremely long, solid nonconducting cylinder has a radius $R_0$. The charge density within the cylinder is a function of the distance $R$ from the axis, given by $\rho_{\mathrm{E}}(R)=\rho_0\left(R / R_0\right)^2$. What is the electric field everywhere inside and outside the cylinder (far away from the ends) in terms of $\rho_0$ and $R_0$ ?

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 $\text{(c) } -d \leq x<0$. Let $\rho_0$ be a positive constant.

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 $x$ (b) outside the slab (at distances much less than the slab's height or breadth). Take the origin at the center of the slab.

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 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.