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. After the terminal speed has been reached, at what rate is electrical energy being converted to thermal energy in the resistance 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. Is the direction of the current induced in the bar from $a$ to $b$ or from $b$ to $a$ ?

A satellite, orbiting the earth at the equator at an altitude of $400 \mathrm{~km}$, has an antenna that can be modeled as a $2.0 \mathrm{~m}$ long rod. The antenna is oriented perpendicular to the earth's surface. At the equator, the earth's magnetic field is essentially horizontal and has a value of $8.0 \times 10^{-5} \mathrm{~T}$; ignore any changes in $B$ with altitude. Assuming the orbit is circular, determine the induced emf between the tips of the antenna.

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.

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.

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 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?

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 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 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 metal rod that is 30.0 cm long expands by 0.0650 cm when its temperature is raised from $0.0^{\circ} C$ to $100.0^{\circ} \mathrm{C}$. A rod of a different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third rod, also 30.0 cm long, is made up of pieces of each of the above metals placed end to end and expands 0.0580 cm between $0.0^{\circ} C$ and $100.0^{\circ} \mathrm{C}$. Find the length of each portion of the composite rod.

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 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?