Giancoli's Physics: Principles with Applications, 7th Edition
20

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

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 49
Q

# 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

1. inside the toroid is $B = \mu_0NI/2 \pi R$, where $N$ is the total number of turns, and
2. outside the toroid is B = 0.
3. 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.
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.
A
1. $B = \dfrac{\mu_o NI}{2\pi R}$
2. $B = 0$
3. 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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