The Earth is surrounded by an electric field, pointing inward at every point, of magnitude $E \approx 150 \mathrm{~N} / \mathrm{C}$ near the surface. (b) How many excess electrons per square meter on the Earth's surface does this correspond to?

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 $2.00 \mathrm{~m}$.

The heating element of a $110~\mathrm{V}, 1500~\mathrm{W}$ heater is $4.2 \mathrm{~m}$ long. If it is made of iron, what must its diameter be?

Near the surface of the Earth, there is a downward electric field of $150 \mathrm{~N} / \mathrm{C}$ and a downward gravitational field of $9.8 \mathrm{~N} / \mathrm{kg}$. A charged $1.0\text{-}\mathrm{kg}$ mass is observed to fall with acceleration $8.0 \mathrm{~m} / \mathrm{s}^2$. Determine the magnitude and sign of its charge.

Near the surface of the Earth, there is a downward electric field of $150 \mathrm{~N} / \mathrm{C}$ and a downward gravitational field of $9.8 \mathrm{~N} / \mathrm{kg}$. A charged $1.0 \mathrm{~kg}$ mass is observed to fall with acceleration $8.0 \mathrm{~m} / \mathrm{s}^2$. What are the magnitude and sign of its charge?

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 $(c) 12.0 \mathrm{~cm}$.

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.

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 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 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 $(b) 7.0 \mathrm{~cm}$.

The electric field between two square metal plates is 130 N/C. The plates are 1.0 m on a side and are separated by 3.0 cm. What is the charge on each plate (assume equal and opposite)? Neglect edge effects.

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 (b) $R_1<R<R_2$. Neglect thickness of shells.