Figure 1 is a sectional view of two circular coils with radius a, each wound with N turns of vire carrying a current I, circulating in the same direction in both coils. The coils are separated by a distance a equal to their radii. In this configuration the coils are called Helmholtz coils; they produce a very uniform magnetic field in the region between them. (a) Derive the expression for the magnitude B of the magnetic field at a point on the axis a distance x to the right of point P, which is midway between the coils. (b) From part (a), obtain an expression for the magnitude of the magnetic at point P. (c) Calculate the magnitude of the magnetic filed at P if N=300 turns, I = 6.00 A and a = 8.00 cm. (d) Calculate dB/dx and d²B/dx² at P (x = 0). Discuss how your results show that the field is very uniform in the vicinity of P.

Figure 1 is a sectional view of two circular coils with radius a, each wound with N turns of vire carrying a current I, circulating in the same direction in both coils. The coils are separated by a distance a equal to their radii. In this configuration the coils are called Helmholtz coils; they produce a very uniform magnetic field in the region between them. (a) Derive the expression for the magnitude B of the magnetic field at a point on the axis a distance x to the right of point P, which is midway between the coils. (b) From part (a), obtain an expression for the magnitude of the magnetic at point P. (c) Calculate the magnitude of the magnetic filed at P if N=300 turns, I = 6.00 A and a = 8.00 cm. (d) Calculate dB/dx and d²B/dx² at P (x = 0). Discuss how your results show that the field is very uniform in the vicinity of P.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Magnetic Forces And Magnetic Fields

Section: Chapter Questions

Problem 36P

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