A metal bar with length $L$, mass $m$, and resistance $R$ is placed on frictionless metal rails that are inclined at an angle $\phi$ above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude $B$ is directed downward as shown in Fig. we saw earlier. The bar is released from rest and slides down the rails.What is the terminal speed of the bar?

A metal bar with length $L$, mass $m$, and resistance $R$ is placed on frictionless metal rails that are inclined at an angle $\phi$ above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude $B$ is directed downward as shown in Fig. we saw earlier. The bar is released from rest and slides down the rails. What is the induced current in the bar when the terminal speed has been reached?

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 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 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 $21 \mu \mathrm{A}$?

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. Calculate the emf induced in the bar.

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 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 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 displacement current density $j_{\mathrm{D}}$ in the air space between the plates?

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 induced magnetic field between the plates at a distance of $2.00 \mathrm{~cm}$ from the axis?

A rectangular loop with width $L$ and a slide wire with mass $m$ are as shown in Fig. we saw earlier. A uniform magnetic field $\vec{B}$ is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of $v_0$ and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligible in comparison to the resistance $R$ of the slide wire. Show that the distance $x$ that the wire moves before coming to rest is $x=m v_0 R / L^2 B^2$.

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 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?

A metal ring 4.50 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.250 T/s. (a) What is the magnitude of the electric field induced in the ring? (b) In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?