In a MHD generator a plasma of conductivity a is driven with velocity u (in the x direction) across a magnetic field B (in the y direction). Two electrode plates, each of area A and separated by a distanced, are placed oriented parallel to the (x, y) plane, as shown in Fig. 9 of Chapter 1.

(a) Show that the open-circuit electric potential difference between the two electrode plates is given by ϕ= Bud

(b) If an external load of resistance R_L is connected between the electrodes, show that the current that flows is given by

where R_p denotes the internal plasma resistance.

(c) Show that the power delivered to the load is

Verify that this power has a maximum (dP_L/dR_L = 0) when R_L = R_p and show that the maximum power that can be delivered to the load is given by

(d) Determine numerical results for items (a), (b), and (c) when B = 1 tesla, u = 100 m/s, σ = 100 mho/m, d = 0.1 m, and A= 1m² .

Figure 9.

Transcribed Image Text:

I = Bud (RL + Rp)