Magnetization curves of hard superconductor samples with non-zero demagnetization factor

We present exact solutions of Bean's critical state model for some sample shapes having non-zero demagnetization factor N. Virgin and hysteresis magnetization curves are obtained for samples in the shape of (i) a sphere (ii) a spheroid (iii) a cylinder of circular cross-section with its axis perpendicular to the field and (iv) a cylinder of elliptical cross section with its axis perpendicular to the field. Some interesting features seen in these first solutions for N ≠ 0 are discussed