A dielectric of permittivity $3.5 \times 10^{-11} \mathrm{F} / \mathrm{m}$ completely fills the volume between two capacitor plates. For t > 0 the electric flux through the dielectric is $\left(8.0 \times 10^{3} \vee \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{3}$. The dielectric is ideal and nonmagnetic; the conduction current in the dielectric is zero. At what time does the displacement current in the dielectric equal $21 \mu \mathrm{A}$?

A slender rod, $0.240 \mathrm{~m}$ long, rotates with an angular speed of $8.80 \mathrm{rad} / \mathrm{s}$ about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of $0.650 \mathrm{~T}$. Suppose instead the rod rotates at $8.80 \mathrm{rad} / \mathrm{s}$ about an axis through its center and perpendicular to the rod. In this case, what is the potential difference between the ends of the rod? Between the center of the rod and one end?

A long, straight solenoid with a cross-sectional area of $8.00 \mathrm{cm}^{2}$ is wound with 90 turns of wire per centimeter, and the windings carry a current of 0.350 A. A second winding of 12 turns encircles the solenoid at its center. The current in the solenoid is turned off such that the magnetic field of the solenoid becomes zero in 0.0400 s. What is the average induced emf in the second winding?

A slender rod, $0.240 \mathrm{~m}$ long, rotates with an angular speed of $8.80 \mathrm{rad} / \mathrm{s}$ about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of $0.650 \mathrm{~T}$. What is the potential difference between its ends?

Suppose that the parallel plates in Fig. we saw earlier have an area of $3.00 \mathrm{~cm}^2$ and are separated by a $2.50$-mm-thick sheet of dielectric that completely fills the volume between the plates. The dielectric has dielectric constant 4.70. (You can ignore fringing effects.) At a certain instant, the potential difference between the plates is $120 \mathrm{~V}$ and the conduction current ic equals $6.00 \mathrm{~mA}$. At this instant, what are the charge $q$ on each plate;

A parallel-plate, air-filled capacitor is being charged as in Fig. we saw earlier. The circular plates have radius $4.00 \mathrm{~cm}$, and at a particular instant the conduction current in the wires is $0.520 \mathrm{~A}$. At $1.00 \mathrm{~cm}$ from the axis?

A very long, cylindrical wire of radius $R$ carries a current $I_0$ uniformly distributed across the cross section of the wire. Calculate the magnetic flux through a rectangle that has one side of length $W$ running down the center of the wire and another side of length $R$, as shown in Fig. we saw earlier.

The slender rod of mass m and length l rotates about the y-axis as the element of a right-circular cone. If the angular velocity about the y-axis is $\omega$, determine the expression for the angular momentum of the rod with respect to the x-y-z axes for the particular position.

The long, straight wire shown in Fig. we saw earlier carries constant current $l$. A metal bar with length $L$ is moving at constant velocity $\overrightarrow{\boldsymbol{v}}$, as shown in the figure. Point $a$ is a distance $d$ from the wire. If the bar is replaced by a rectangular wire loop of resistance $R$, what is the magnitude of the current induced in the loop?

A parallel-plate, air-filled capacitor is being charged as in Fig. we saw earlier. The circular plates have radius $4.00 \mathrm{~cm}$, and at a particular instant the conduction current in the wires is $0.520 \mathrm{~A}$. What is the rate at which the electric field between the plates is changing?

A parallel-plate air-filled capacitor having area 40 cm$^2$ and plate spacing 1.0 mm is charged to a potential difference of 600 V. Find the capacitance.

A parallel-plate air-filled capacitor having area $40 \mathrm{~cm}^2$ and plate spacing $1.0 \mathrm{~mm}$ is charged to a potential difference of $600 \mathrm{~V}$. Find the capacitance ?

A parallel-plate air-filled capacitor having area 40 cm$^2$ and plate spacing 1.0 mm is charged to a potential difference of 600 V. Find the stored energy.

A parallel-plate air-filled capacitor having area 40 cm$^2$ and plate spacing 1.0 mm is charged to a potential difference of 600 V. Find the electric field between the plates.