CP CALC We have ignored the variation of the magnetic

Chapter 30, Problem 30.73

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CP CALC We have ignored the variation of the magnetic field across the cross section of a toroidal solenoid. Lets now examine the validity of that approximation. A certain toroidal solenoid has a rectangular cross section (Fig. P30.73). It has N uniformly spaced turns, with air inside. The magnetic field at a point inside the toroid is given by the equation derived in Example 28.10 (Section 28.7). Do not assume the field is uniform over the cross section. (a) Show that the magnetic flux through a cross section of the toroid is (b) Show that the inductance of the toroidal solenoid is given by L = m0N2 h 2p lna b a b (c) The fraction may be written as Use the power series expansion valid for to show that when is much less than a, the inductance is approximately equal to Compare this result with the result given in Example 30.3 (Section 30.2).