An infinite straight wire with a cross sectional area a 2 carries a low frequency current I(t)
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An infinite straight wire with a cross sectional area πa2 carries a low frequency current I(t) = I0 cos ωt. Without close inspection, it is impossible to tell if the wire is broken into two pieces with a tiny gap of width b << a separating the two because the displacement current flowing in the gap is exactly equal to I (t). Confirm this by calculating the displacement current Id (t) from the electric field in the gap.
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