The Earth is surrounded by an electric field, pointing inward at every point, of magnitude $E \approx 150 \mathrm{~N} / \mathrm{C}$ near the Earth's surface. What is the net charge on the Earth?

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?

Two long straight parallel wires are $18 \mathrm{~cm}$ apart. Wire A carries $3.0 \mathrm{~A}$ current. Wire $B$'s current is $6.0 \mathrm{~A}$ in the same direction. Determine the force on wire ${A}$ due to wire $B$, and the force on wire $B$ due to wire ${A}$. Are these two forces equal and opposite? Why or why not?

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 the two conducting plates in Problem 24 have the same sign and magnitude of charge. (b) What then will be the electric field outside them on either side?

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.

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 $Q=5.50 \mu \mathrm{C}$ rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at a point (b) $6.00 \mathrm{~cm}$ from the center of the cavity.

A long thin wire, hundreds of meters long, carries a uniformly distributed charge of $-7.2 \mu \mathrm{C}$ per meter of length. Estimate the magnitude and direction of the electric field at points (a) $5.0 \mathrm{~m}$.

A long thin wire, hundreds of meters long, carries a uniformly distributed charge of $-8.4 \mu \mathrm{C}$ per meter of length. Estimate the magnitude and direction of the electric field at point $1.5 \mathrm{~m}$, perpendicular from the center of the wire.

In a certain region of space, the electric field is constant in direction (say horizontal, in the $x$ direction). but its magnitude decreases from $E=650 \mathrm{~N} / \mathrm{C}$ at $x=0$ to $E=370 \mathrm{~N} / \mathrm{C}$ at $x=25 \mathrm{~m}$. Determine the charge within a cubical box of side $\ell=25 \mathrm{~m}$, where the box is oriented so that four of its sides are parallel to the field lines.

A uniform electric field of magnitude $5.8 \times 10^2 \mathrm{~N} / \mathrm{C}$ passes through a circle of radius $13 \mathrm{~cm}$. What is the electric flux through the circle when its face is $(a)$ perpendicular to the field lines?

A dipole consists of charges $+e$ and $-e$ separated by $0.68 \mathrm{~nm}$. It is in an electric field $E=2.2 \times 10^4 \mathrm{~N} / \mathrm{C}$. What is the work required to rotate the dipole from being oriented parallel to the field to being antiparallel to the field?

A dipole consists of charges $+e$ and $-e$ separated by $0.68 \mathrm{~nm}$. It is in an electric field $E=2.2 \times 10^4 \mathrm{~N} / \mathrm{C}$. What is the torque on the dipole when it is perpendicular to the field?

An electron is traveling through a uniform electric field. The field is constant and given by $\overrightarrow{\mathbf{E}}=$ $\left(2.00 \times 10^{-11} \mathrm{~N} / \mathrm{C}\right) \hat{\mathbf{i}}-\left(1.20 \times 10^{-11} \mathrm{~N} / \mathrm{C}\right) \hat{\mathbf{j}}$. At $t=0$, the electron is at the origin and traveling in the $x$ direction with a speed of $1.90 \mathrm{~m} / \mathrm{s}$. What is its position $2.00$ s later?