A toroid is a solenoid in the shape of a donut (Fig. 20–60). Use Ampère’s law along the circular paths, shown dashed in Fig. 20–60a, to determine that the magnetic field a) inside the toroid is B = \mu_0NI/2 \pi R, where N is the total number of turns, and b) outside the toroid is B = 0. c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

a) B = \dfrac{\mu_o NI}{2\pi R} b) B = 0 c) Since the field is proportional to \dfrac{1}{R}, it is not uniform across the width of the torroid. It changes with distance from the center.

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Giancoli's Physics: Principles with Applications, 7th Edition

Magnetism

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20-3: Force on Electric Current in Magnetic Field

20-4: Force on Charge Moving in Magnetic Field

20-5 and 20-6: Magnetic Field of Straight Wire, Force between Two Wires

20-7: Solenoids and Electromagnets

20-8: Ampère's Law

20-9 and 20-10: Torque on Curent Loop, Motors, Galvanometers

20-11: Mass Spectrometer

20-12: Ferromagnetism, Hysteresis

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Problem 49

A toroid is a solenoid in the shape of a donut (Fig. 20–60). Use Ampère’s law along the circular paths, shown dashed in Fig. 20–60a, to determine that the magnetic field

inside the toroid is $B = \mu_0NI/2 \pi R$ , where $N$ is the total number of turns, and
outside the toroid is B = 0.
Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

Figure 20-60 (a) A toroid or torus.

Problem 49. (b) A section of the toroid showing direction of the current for three loops: a dot means current toward you, and a cross means current away from you.

Figure 20-60 (b) A section of the toroid showing direction of the current for three loops:

\odot

means current toward you, and

\otimes

means current away from you.

$B = \dfrac{\mu_o NI}{2\pi R}$
$B = 0$
Since the field is proportional to $\dfrac{1}{R}$ , it is not uniform across the width of the torroid. It changes with distance from the center.

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