Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. For example, they are traditionally used in the experiment for the measurement of the charge-to-mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius and also carry equal currents in the same direction, as shown in the figure. Suppose the radius of the coils is R = 13.50 cm and each coil carries a current of I = 10.50 A and has N = 300.0 turns. The coils are in the yz plane where one coil's center is at x = 0 the other coil's center is at x = R. Using the Biot-Savart law, determine the expression for the resultant magnetic field B, along the line x joining their centers. Express the magnetic field in terms of the radius of the coils R, the number of turns N, the current I, x, and the permeability of free space, µo. B, = 00 Evaluate the magnetic field B, at x = 3.375 cm (†R) and x = 10.13 cm (R). В, (3.375) — T Bz (10.13) = T

Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. For example, they are traditionally used in the experiment for the measurement of the charge-to-mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius and also carry equal currents in the same direction, as shown in the figure. Suppose the radius of the coils is R = 13.50 cm and each coil carries a current of I = 10.50 A and has N = 300.0 turns. The coils are in the yz plane where one coil's center is at x = 0 the other coil's center is at x = R. Using the Biot-Savart law, determine the expression for the resultant magnetic field B, along the line x joining their centers. Express the magnetic field in terms of the radius of the coils R, the number of turns N, the current I, x, and the permeability of free space, µo. B, = 00 Evaluate the magnetic field B, at x = 3.375 cm (†R) and x = 10.13 cm (R). В, (3.375) — T Bz (10.13) = T

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter12: Sources Of Magnetic Fields

Section: Chapter Questions

Problem 35P: When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0104 T....

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