An infinite straight wire with a cross sectional area a 2 carries a low frequency current I(t) = I 0 cos t. Without close inspection,

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 I_d (t) from the electric field in the gap.