A longitudinal AC magnetic field B(t ) = zB 0 cos t is driven through the interior

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A longitudinal AC magnetic field B(t ) = ẑB0 cos ωt is driven through the interior of an ohmic tube with length L and radius R << L.

(a) Find the low-frequency eddy-current density inside the tube, neglecting the effects of self-inductance.
(b) Find the correction to the eddy-current density produced by self-inductance (to next order in ω).
(c) Derive the condition where the correction in part (b) can be ignored.

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