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 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 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 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 $x=m v_0 R / L^2 B^2$.

The square loop shown in Figure mentioned moves into a $0.80 \mathrm{~T}$ magnetic field at a constant speed of $10 \mathrm{~m} / \mathrm{s}$. The loop has a resistance of $0.10 \Omega$, and it enters the field at $t=0 \mathrm{~s}$.

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 solenoid has 585 turns per meter and a cross-sectional area of $2.70 \mathrm{~cm}^2$. The current through the windings as a function of time is $\left(0.600 \mathrm{~A} / \mathrm{s}^2\right) t^2$. A wire loop of resistance $0.600 \Omega$ is around the solenoid, parallel with its coils, and centered on the axis of the solenoid. What is the current induced in the loop at $t=13.9 \mathrm{~s}$ ?

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?