We consider a collisionless plasma withE(the electric field) parallel to the y‐axis of a cartesian frame of reference andB(the magnetic induction) parallel to the z‐axis. When there is a gradient, orthogonal toB, of the quantity ϵE², where ϵ = 1 + 4πρmc²/B², where ρmis the plasma mass density and c the speed of light, there is driven a (dielectric) current (j) given in the following two cases, byj=▽(ϵE2)c/B.(i) When▽(ϵE²) is parallel toE,jis in the direction ofE×B, and (ii) when▽(ϵE²) is in the directionE×B,jis in the direction ofE. In the former case it follows that, in a steady state,p⊥+B2/8π−ϵE2/8π=constantalong a line in the y‐direction, and in the latter casep⊥+B2/8π+ϵE2/8π=constanton a line in the x‐direction where p⊥is the pressure perpendicular toB. The currents related to ϵE² are geophysically significant in the region of interaction of the solar wind and geomagnetic field in the low latitude boundary layer and geomagnetic tail. The last written equation enables a realistic estimate
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