Should the surface of a computer disk be made from a hard or a soft ferromagnetic substance?

A current in a solenoid having air in the interior creates a magnetic field $\mathbf{B}=\mu_0 \mathbf{H}$. Describe qualitatively what happens to the magnitude of $\mathbf{B}$ as (a) aluminum, (b) copper, and (c) iron are placed in the interior:

Figure is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is surrounded by another rubber layer. In a particular application, the current in the inner conductor is $1.00 \mathrm{~A}$ out of the page and the current in the outer conductor is $3.00 \mathrm{~A}$ into the page. Determine the magnitude and direction of the magnetic field at points $a$ and $b$.

Discuss the difference among ferromagnetic, paramagnetic, and diamagnetic substances.

Explain the significance of the Curie temperature for a ferromagnetic substance.

A long, straight wire lies on a horizontal table and carries a current of 1.20 $\mu A$. In a vacuum, a proton moves parallel to the wire (opposite the current) with a constant speed of $2.30 \times 104$ m/s at a distance d above the wire. Ignoring the magnetic field due to the Earth, determine the value of d.

Four long, parallel conductors carry equal currents of $I=5.00 \mathrm{~A}$. The given figure is an end view of the conductors. The current direction is into the page at points $A$ and $B$ and out of the page at points $C$ and $D$. Calculate the direction of the magnetic field at point $P$, located at the center of the square of edge length $\ell=0.200 \mathrm{~m}$.

Four long, parallel conductors carry equal currents of I=5.00 A. The figure is an end view of the conductors. The current direction is into the page at points $A$ and $B$ (indicated by the crosses) and out of the page at $C$ and $D$ (indicated by the dots). Calculate the magnitude of the magnetic field at point $P$, located at the center of the square of edge length $0.200 \mathrm{~m}$.

Why can the effect of diamagnetism be neglected in a paramagnetic substance?

The unit of magnetic flux is named for Wilhelm Weber. The practical-size unit of magnetic field is named for Johann Karl Friedrich Gauss. Both were scientists at Gottingen, Germany. Along with their individual accomplishments, together they built a telegraph in 1833. It consisted of a battery and switch, at one end of a transmission line $3 \mathrm{~km}$ long, operating an electromagnet at the other end. (Andre Ampere suggested electrical signaling in 1821; Samuel Morse built a telegraph line between Baltimore and Washington in 1844.) Suppose that Weber and Gauss's transmission line was as diagrammed in the figure. Two long, parallel wires, each having a mass per unit length of $40.0 \mathrm{~g} / \mathrm{m}$, are supported in a horizontal plane by strings $6.00 \mathrm{~cm}$ long. When both wires carry the same current $I$, the wires repel each other so that the angle $\theta$ between the supporting strings is $16.0^{\circ}$. (a) Are the currents in the same direction or in opposite directions? (b) Find the magnitude of the current.

Why is the susceptibility of a diamagnetic substance negative?

A lightning bolt may carry a current of $1.00 \times 10^t \mathrm{~A}$ for a short period of time. What is the resulting magnetic field $100 \mathrm{~m}$ from the bolt? Suppose that the bolt extends far above and below the point of observation.

A current in a conductor produces a magnetic field that can be calculated using the Biot–Savart law. Because current is defined as the rate of flow of charge, what can you conclude about the magnetic field produced by stationary charges? What about that produced by moving charges?

Three long wires (wire 1 , wire 2 , and wire 3) hang vertically. The distance between wire 1 and wire 2 is $20.0 \mathrm{~cm}$. On the left, wire 1 carries an upward current of $1.50 \mathrm{~A}$. To the right, wire 2 carries a downward current of $4.00 \mathrm{~A}$.