Chapter 26, Problem 89PP

A toroid is a solenoid-like coil bent into a circle (Fig. 26.52a). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us with an almost unlimited energy source using deuterium fuel extracted from seawater.

The ITER consortium, an international collaboration, is building a large toroidal fusion experiment in France; it’s expected to be the first fusion device to produce energy on a large scale. Figure 26.52b shows a cross section of a toroid, with current emerging from the page at the inner edge and descending at the outer edge. The black circle is an Ampèrian loop.

FIGURE 26.52 Diagram of (a) a toroidal coil and (b) a cross section of the coil (Passage Problems 88–91)

88. The magnetic field associated with the toroid is nonzero

1. a. only within the “hole” in the donut-shaped coil.
2. b. only within the region bounded by the coils.
3. c. only outside the coils.
4. d. everywhere.

89. In Fig. 26.52b, the magnetic field lines must be

1. a. straight, and pointing into the page.
2. b. straight, and pointing out of the page.
3. c. straight, and pointing radially.
4. d. circular.

90. Doubling the total number of turns N in the toroid, without changing its size or the current, will

1. a. double the magnetic field.
2. b. quadruple the magnetic field.
3. c. halve the magnetic field.
4. d. not change the magnetic field.

91. The toroid has inner radius R_in and outer radius R_out, while r is the radial coordinate measured from the center. The toroid is made from wire wound into a total of N turns, and carries current I. Which of the following is the correct formula for the magnetic field within the coils?

1. a. B = μ₀NI
2. b. B = μ₀NI/2πR_in
3. c. B = μ₀NI/2πR_out
4. d. B = μ₀NI/2πr