Consider the Helmholtz coil configuration shown in Fig. 2. Here R = 0.2 in, I =

Question

Consider the Helmholtz coil configuration shown in Fig. 2. Here R = 0.2 in, I = 10 A. and there are N = 100 windings in each coil. You can neglect the thickness of each coils windings so that its dimensions are hilly specified by R. (a) Use Biot and Savart?s law to derive an expression for the magnetic field as a function of displacement x from the center of the coils. (b) Calculate the strength of the magnetic field in Tesla at the central point between the coils where x = 0 and for x = plus minus R/2 and make a plot of B(x).

Explanation / Answer

The Biot-Savart law for the magnetic field generated by a current I is dB = (mu_0/4pi) I (dl x r) |r|^-3, where dl and r are vectors, and x is the cross product among them. dl has the same orientation of the current. The total magnetic field B is given by the integral B = Integral dB over the whole circuit carrying current I. In this case, I has to be multiplied by the number of windings N. It easy to see that the field is axially directed along the x axis.

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