Helmholtz Coils. Figure P28.67 is a sectional view of two

Chapter 28, Problem 28.67

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Helmholtz Coils. Figure P28.67 is a sectional view of two circular coils with radius a, each wound with N turns of wire 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) Graph B versus x for x = 0 to x = a>2. Compare this graph to one for the magnetic field due to the righthand coil alone. (c) From part (a), obtain an expression for the magnitude of the magnetic field at point P. (d) Calculate the magnitude of the magnetic field at P if N = 300 turns, I = 6.00 A, and a = 8.00 cm. (e) Calculate dB>dx and d2 B>dx2 at P1x = 02. Discuss how your results show that the field is very uniform in the vicinity of P

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