Penetration of time-varying magnetic field B_sw(panels a, c, e) and associated Ohmic heating Q (panels b, d, f) in the case of a constant σ_P atmospheric layer of 1000 km, subject to a time-varying magnetic field of 4 mG imposed as a boundary condition at the top of the layer. The Hall conductivity is neglected here (σ_H = 0) and the Pedersen conductivity is constant in space. The dotted black line in panels a, c and e correspond to the strength of the external time-varying magnetic field B_sw. Panels a and b show cases with constant skin-depth δ_P and different (σ_p, P_orb) as indicated in the legend (note that in panel a, all lines are superposed). In panel a, the skin-depth δ_P (which is the typical length-scale over which B_sw penetrates in the atmosphere) is highlighted. Note: the value of δ_P in each case is shown by the vertical colored dashed lines in the upper panels (see text). Panel c and d depict cases with the same σ_P =0.5 S/m but different P_orb. Panels e and f show cases with the same P_orb =1 day but different values of σ_P.