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When an electromagnetic wave enters the ionised region of the ionosphere, the moving electron cloud gives rise to a space current, while the electric field also produces a capacitive displacement current. In this situation, what is the phase relation between the space current and the displacement current?

1. The space current is in phase with the displacement current.
2. The space current lags the displacement current by 180°.
3. The space current lags the displacement current by 90°.
4. The space current leads the displacement current by 90°.

Correct answer: The space current lags the displacement current by 180°.

Solution

For E = E0 sin(wt), the displacement current J_d = e0 dE/dt ~ +cos(wt). The free electron obeys m dv/dt = -eE, giving v ~ +cos(wt) and conduction (space) current J = -nev ~ -cos(wt). So the space current is 180 deg (anti-phase) relative to the displacement current.

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