Figure 1 is a sectional view of two circular coils with radius a, each wound with N turns of wire carrying a current 1, 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 wire carrying a current 1, 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.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter31: Gauss’s Law For Magnetism And Ampère’s Law

Section: Chapter Questions

Problem 72PQ

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