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 $2.00 \mathrm{~m}$.

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 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).

If a proton $\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$ revolves in a circular orbit of radius $R=7.0 \mathrm{~cm}$ about the axis (i.e., between the cylinders), what must be its speed?

A thin cylindrical shell of radius $R_1=4.5 \mathrm{~cm}$ is surrounded by a second cylindrical shell of radius $R_2=9.0 \mathrm{~cm}$. Both cylinders are $5.0 \mathrm{~m}$ long and the inner one carries a total charge $Q_1=-0.88 \mathrm{nC}$ and the outer one $Q_2=+1.56 \mathrm{nC}$. For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of $(c) 12.0 \mathrm{~cm}$.

If an electron $\left(m=9.1 \times 10^{-31} \mathrm{~kg}\right)$ escaped from the surface of the inner cylinder in Problem 36 with negligible speed, what would be its speed when it reached the outer cylinder?

A thin cylindrical shell of radius $R_1=4.5 \mathrm{~cm}$ is surrounded by a second cylindrical shell of radius $R_2=9.0 \mathrm{~cm}$. Both cylinders are $5.0 \mathrm{~m}$ long and the inner one carries a total charge $Q_1=-0.88 \mathrm{nC}$ and the outer one $Q_2=+1.56 \mathrm{nC}$. For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of $(a) 3.0 \mathrm{~cm}$.

A thin cylindrical shell of radius $R_1$ is surrounded by a second concentric cylindrical shell of radius $R_2$. The inner shell has a total charge $+Q$ and the outer shell $-Q$. Assuming the length $\ell$ of the shells is much greater than $R_1$ or $R_2$, determine the electric field as a function of $R$ (the perpendicular distance from the common axis of the cylinders) for (a) $0<R<R_1$. Neglect thickness of shells.

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?

A thin cylindrical shell of radius $R_1=6.5 \mathrm{~cm}$ is surrounded by a second cylindrical shell of radius $R_2=9.0 \mathrm{~cm}$. Both cylinders are $5.0 \mathrm{~m}$ long and the inner one carries a total charge $Q_1=-0.88 \mu \mathrm{C}$ and the outer one $Q_2=+1.56 \mu \mathrm{C}$. For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of (c) $12.0 \mathrm{~cm}$.

A solid metal cube has a spherical cavity right at its center. At the center of the cavity there is a point charge $Q=+8.00 \mu \mathrm{C}$. The metal cube carries a net charge $q=-6.40 \mu \mathrm{C}$ (not including $Q$ ). Determine the total charge on the surface of the spherical cavity.

A thin cylindrical shell of radius $R_1=6.5 \mathrm{~cm}$ is surrounded by a second cylindrical shell of radius $R_2=9.0 \mathrm{~cm}$, as in Fig. $22-35$. Both cylinders are $5.0 \mathrm{~m}$ long and the inner one carries a total charge $Q_1=-0.88 \mu \mathrm{C}$ and the outer one $Q_2=+1.56 \mu \mathrm{C}$. For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of $(b) 7.0 \mathrm{~cm}$.

A thin cylindrical shell of radius $R_1=4.5 \mathrm{~cm}$ is surrounded by a second cylindrical shell of radius $R_2=9.0 \mathrm{~cm}$. Both cylinders are $5.0 \mathrm{~m}$ long and the inner one carries a total charge $Q_1=-0.88 \mathrm{nC}$ and the outer one $Q_2=+1.56 \mathrm{nC}$. For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of $(b) 7.0 \mathrm{~cm}$.

A spherical cavity of radius $4.50 \mathrm{~cm}$ is at the center of a metal sphere of radius $18.0 \mathrm{~cm}$. A point charge $Q=6.50 \mu \mathrm{C}$ rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at a point $3.00 \mathrm{~cm}$ from the center of the cavity.