Magnetohydrodynamic generator analysis · CAP 2005 #26
Physics · electromagnetism
Problem
A magnetohydrodynamic (MHD) generator is a device that converts part of the kinetic energy of a streaming hot gas into electrical energy. At its operating temperature of between 2000 and 3000 K, the gas is readily ionised. As schematically shown in the figure, the ions and electrons enter a region between two electrodes (here, parallel conducting plates of area A separated by a gap d) in which a uniform and constant magnetic field B has been set up, pointing straight out of the page. Their initial velocity v is parallel to the plates. A resistor R is connected to the plates. The magnetic field is strong enough that many charged particles will hit the electrodes and charge them before they can exit. This creates a time-varying potential difference V between the plates.
[Figure: Diagram showing parallel plates with gap d, magnetic field B pointing out of page, particles with velocity v parallel to plates, and resistor R connected between plates]
(a) On a diagram, display all the forces acting on a positive ion at some generic position between the plates. Use your diagram to show that the ion experiences a braking force as soon as its velocity has a component transverse to the plates.
(b) Then, as a crude approximation, assume that any electric field E arising from the process is uniform everywhere between the plates. Assume also that the transverse component of the velocity of the charges remains everywhere much smaller than its longitudinal component.