## Abstract

The effect of an alined magnetic field H$_\infty$ on the lifting force, experienced by a flat plate at incidence in a conducting field, is examined with respect to variations in the conductivity $\sigma$ and in H$_\infty$. The governing integral equation does not possess a unique solution unless the velocity (and pressure) are required to be finite either at the trailing edge or at the leading edge of the plate. It is then solved numerically for various finite values of $\sigma$ and its asymptotic behaviour is examined analytically. The conclusions are: If the undisturbed fluid velocity V > H$_\infty$/(4$\mu\rho$)$^\frac{1}{2}$, the Alfven speed, whichever side condition is imposed at finite $\sigma$, the solution as $\sigma\rightarrow\infty$ formally satisfies the same condition. If V < H$_\infty$/(4$\pi\rho$)$^\frac{1}{2}$ and the velocity is required to be finite at the trailing edge, as $\sigma\rightarrow\infty$ the velocity formally becomes finite at the leading edge and develops a quasisingular behaviour at the trailing edge. On the other hand, if V < H$_\infty$/(4$\pi\rho$)$^\frac{1}{2}$ and the velocity is required to be finite at the leading edge the solution appears to become pathological as $\sigma \rightarrow \infty$. In the critical case V = H$_\infty$/(4$\pi\rho$)$^\frac{1}{2}$ the solution is unique for all $\sigma$ < $\infty$ and in the limit solution the velocity must be finite at the trailing edge. The theory here is also relevant to the Oseen flow past an inclined flat plate. Finally, it is shown that if the velocity is required to be finite at the leading edge then the solution of the integral equation becomes singular at at least one value of $\sigma$ for all H$_\infty$ such that H$^2_\infty$ > 0.906(4$\pi\rho V^2$).