Chapter 22: Magnetism

Volcanic and other such activity at the mid-Atlantic ridge extrudes material to fill the gap between separating tectonic plates associated with continental drift. The magnetization of rocks is found to reverse in a coordinated manner with distance from the ridge. What does this imply about the Earth’s magnetic field and how could the knowledge of the spreading rate be used to give its historical record?

What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases shown in Figure 22.50 below.

Make a drawing and use RHR-2 to find the direction of the magnetic field of a current loop in a motor (such as in Figure 22.34). Then show that the direction of the torque on the loop is the same as produced by like poles repelling and unlike poles attracting.

A mass spectrometer is being used to separate common oxygen $-16$ from the much rarer oxygen $-18$, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) The ratio of the masses of these two ions is $16$ to $18$, the mass of oxygen$-16$ is $2.66\times 10^{-26}\mathrm{k}\mathrm{g}$, and they are singly charged and travel at $5.00\times 10{}^6\mathrm{m}/\mathrm{s}$ in a $1.20-\mathrm{T}$ magnetic field. What is the separation between their paths when they hit a target after traversing a semicircle?

Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?

(a) Triply charged uranium-$235$ and uranium-$238$ ions are being separated in a mass spectrometer. (The much rarer uranium-$235$ is used as reactor fuel.) The masses of the ions are $3.90\times 10^{-25}\mathrm{k}\mathrm{g}$ and $3.95\times 10^{-25}\mathrm{k}\mathrm{g}$, respectively, and they travel at $3.00\times 10^5\mathrm{m}/\mathrm{s}$ in a $0.250-\mathrm{T}$ field. What is the separation between their paths when they hit a target after traversing a semicircle? (b) Discuss whether this distance between their paths seems to be big enough to be practical in the separation of uranium-$235$ from uranium-$238$.

The force on the rectangular loop of wire in the magnetic field in Figure 22.56 can be used to measure field strength. The field is uniform, and the plane of the loop is perpendicular to the field. (a) What is the direction of the magnetic force on the loop? Justify the claim that the forces on the sides of the loop are equal and opposite, independent of how much of the loop is in the field and do not affect the net force on the loop. (b) If a current of 5.00 A is used, what is the force per tesla on the 20.0-cm-wide loop?

Figure 22.56 A rectangular loop of wire carrying a current is perpendicular to a magnetic field. The field is uniform in the region shown and is zero outside that region.

(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength?

(b) How many percent would the current need to be increased to return the torque to original values?

If you have three parallel wires in the same plane, as in Figure 22.48, with currents in the outer two running in opposite directions, is it possible for the middle wire to be repelled by both? Attracted by both? Explain.

A large water main is $2.50\mathrm{m}$ in diameter and the average water velocity is$$\begin{gathered} 6.00\mathbf{m}/\phantom{\mathbf{m}\mathbf{s}} \\ \mathbf{s} \end{gathered}$$.Find the Hall voltage produced if the pipe runs perpendicular to the Earth’s $5.00\times 10^{-5}-\mathrm{T}$ field.