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 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.

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 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. Calculate the emf induced in the bar.

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 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?

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 parallel-plate capacitor with area 0.200 m$^2$ and plate separation of 3.00 mm is connected to a 6.00-V battery. What is the electric field between the plates?

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 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 slender rod, 0.240 m long, rotates with an angular speed of 8.80 rad/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 T. (a) What is the induced emf in the rod? (b) What is the potential difference between its ends? (c) Suppose instead the rod rotates at 8.80 rad/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?

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.