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.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

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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.

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