The electron beam in a certain cathode ray tube possesses cylindrical symmetry, and the charge density is represented by $\rho_{v}=-0.1 /\left(\rho^{2}+10^{-8}\right) \mathrm{p} \mathrm{C} / \mathrm{m}^{3}$ for $0<\rho<3 \times 10^{-4} \mathrm{m}, \text { and } \rho_{v}=0 \text { for } \rho>3 \times 10^{-4} \mathrm{m}.$ (a) Find the total charge per meter along the length of the beam; (b) if the electron velocity is $5 \times 10^{7} \mathrm{m} / \mathrm{s},$ and with one ampere defined as 1C/s, find the beam current.

What were the causes and effects of the Thirty Years' War?

How did World War II's actors and their goals and strategies compare with those of World War I?

A uniform volume charge density of $0.2 \mu \mathrm{C} / \mathrm{m}^{3}$ is present throughout the spherical shell extending from r = 3 cm to r = 5 cm. If $\rho_{v}=0$ elsewhere, find (a) the total charge present throughout the shell, and (b) $r_1$ if half the total charge is located in the region $3 cm < r < r_1.$

Electrons are in random motion in a fixed region in space. During any $1 \mu \mathrm{s}$ interval, the probability of finding an electron in a subregion of volume $10^{-15} \mathrm{m}^{2}$ is 0.27. What volume charge density, appropriate for such time durations, should be assigned to that subregion?

A charge $Q_0$ located at the origin in free space produces a field for which $E_{z}=1 \mathrm{kV} / \mathrm{m}$ at point P(−2, 1, −1). (a) Find $Q_0.$ Find E at M(1, 6, 5) in (b) rectangular coordinates; (c) cylindrical coordinates; (d) spherical coordinates.

A charge of −1 nC is located at the origin in free space. What charge must be located at (2, 0, 0) to cause $E_x$ to be zero at (3, 1, 1)?

A crude device for measuring charge consists of two small insulating spheres of radius a, one of which is fixed in position. The other is movable along the x axis and is subject to a restraining force kx, where k is a spring constant. The uncharged spheres are centered at x = 0 and x = d, the latter fixed. If the spheres are given equal and opposite charges of Q/C, obtain the expression by which Q may be found as a function of x. Determine the maximum charge that can be measured in terms of $\epsilon_{0}, k,$ and d, and state the separation of the spheres then. What happens if a larger charge is applied?

Recall that an allusion is a reference to historical, literary, or cultural details outside of a literary work. Reread lines 118-122 of "The Condition of England." What point is Carlyle making with his allusion to Midas in these lines?

A 100-nC point charge is located at A(−1, 1, 3) in free space. (a) Find the locus of all points P(x, y,z) at which $E_{x}=500 \mathrm{V} / \mathrm{m}.$ (b) Find $y_1$ if $P\left(-2, y_{1}, 3\right)$ lies on that locus.

The electric flux density in free space is given by D = y$^2$a$_{\text{x}}$ + 2xya$_{\text{y}}$ - 4za$_{\text{z}}$ nC/m$^2$ (a) Find the volume charge density. (b) Determine the flux through surface x = 3,0 < y < 6,0 < z < 5.

The surfaces $\rho=3, \rho=5, \phi=100^{\circ}, \phi=130^{\circ}, z=3, \text { and } z=4.5$ define a closed surface. Find (a) the enclosed volume; (b) the total area of the enclosing surface; (c) the total length of the twelve edges of the surfaces; (d) the length of the longest straight line that lies entirely within the volume.

Two point charges of equal magnitude q are positioned at $z=\pm d / 2.$ (a) Find the electric field everywhere on the z axis; (b) find the electric field everywhere on the x axis; (c) repeat parts (a) and (b) if the charge at z = −d/2 is −q instead of +q.

Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?). (b) Repeat part (a) for two point charges having opposite signs.