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The toroid is a coil of wire wrapped around a doughnut-shaped ring made of nonconducting material. Toroidal magnetic fields are used to confine fusion plasmas.

a. From symmetry, what must be the shape of the magnetic field in this toroid? Explain.

b. Use Ampere's law to find an expression for the magnetic field strength at a distance from the axis of a toroid with closely spaced turns carrying current

c. Is a toroidal magnetic field a uniform field? Explain.

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Rochelle Enrera
Rochelle EnreraLv10
1 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A toroid is a coil of wire wrapped around adoughnut-shapedring (a torus). For a tightly
wrapped toroid with N turns, the magnetic field lines of Bformconcentric circles inside the
toroid, and the field is zero outside. Use Ampere’s law to find an expression for the magnetic
field strength B at a radial position r from the axis ofthetoroid.

Learning Goal: 

To apply Ampère's law to find the magnetic field inside an infinite solenoid. 

In this problem we will apply Ampère's law, written 

to calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). The segment of the solenoid shown in (Figure 1) has length L, diameter D, and n turns per unit length with each carrying current I. It is usual to assume that the component of the current along the z-axis is negligible. (This may be assured by winding two layers of closely spaced wires that spiral in opposite directions.) 

From symmetry considerations, it is possible to show that far from the ends of the solenoid, the magnetic field is axial.

a) What is Iencl, the current passing through the chosen loop? Express your answer in terms of L (the length of the Amperean loop along the axis of the solenoid) and other variables given in the introduction.

b) Find Bin, the z component of the magnetic field inside the solenoid where Ampere's law applies. Express your answer in terms of L, D, n, I, and physical constants such as μ0.

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