Helmholtz coils are two identical circular coils having

Chapter 28, Problem 28.61

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Helmholtz coils are two identical circular coils having thesame radius R and the same number of turns N, separatedby a distance equal to the radius R and carrying the samecurrent I in the same direction. (See Fig. 28-58.) They areused in scientific instruments to generate nearly uniformmagnetic fields.(They can be seen in the photo, Fig. 27-18.)(a) Determine the magnetic field B at points x along the linejoining their centers. Let x = 0 at the center of one coil, andx = R at the center of the other, (b) Show that the fieldmidway between the coils is particularly uniform bydB d2Bshowing that = 0 and - = 0 at the midpoint betweendx d x2the coils, (c) If R = 10.0 cm, N = 250 turns and I = 2.0 A,what is the field at the midpoint between thecoils, x = R / 2?FIGURE 28-58 61.

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