Answer of Consider a Fat Long Straight Wire…

fat long straight wire

Answer of Consider a fat long straight wire… for $9 Only

Consider a fat long straight wire, with cross-sectional radius a, that carries a constant current I, uniformly distributed over its cross section. A narrow gap along the length of the wire, of length w ≪ a, forms a parallel-plate capacitor from the two exposed faces of the wire, as shown in the figure below. This means that the current I is adding charge to the left face and removing charge from the right face of the capacitor.
(a) Find the electric and magnetic fields in the gap, as functions of the distance s from the wire’s horizontal axis and the time t, for s ≤ a. Assume the charge on the exposed faces of the wire is zero at t = 0.
(b) Find the energy density uem in the gap as a function of s and t.
(c) Find the Poynting vector S in the gap as a function of s and t.
(d) Check that local energy continuity is satisfied within the gap, i.e., that ∂uem/∂t = −~∇ · ~S.

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