Conductivities, penetration and Ohmic heating in the atmospheres of Trappist-1 b (top panels) and π Men c (bottom panels). Left panels (a and d) represent the parallel (dotted gray lines), Hall (dashed colored lines) and Pedersen (solid colored lines) conductivities as a function of pressure in the atmosphere. Four values of planetary magnetic field (B_P = 1 mG, 10 mG, 0.2 G, 4G) are represented in all panels by the blue, orange, green and red lines, respectively. The middle panels (b and e) show the penetrating magnetic field normalized to B_sw. The right panels (c and f) show the profile of the associated Ohmic heating Q (Eq. (13)) for B_sw = 1 G (solid lines) and B_sw = 10 G (dotted lines). The black dashed line show the heating rate from photochemistry in the underlying atmospheric model (García Muñoz 2023). Calculations have been done using the orbital period of the planet for Trappist-1 b and π Men c (see Table 1).